HlNH HQC]2 - f.libvui.comf.libvui.com/dlsm12/ThietKeBaiGiangHinhHoc12_ba88b1d7a7.pdf · trong chifcfng trinh Hin nhih hp cafc 1c hin2 h da dien deu, ...Da la nhuhy hing h ma khi iing

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W.V-'

TRAN V I N H

I hiet ke bai giang

HlNH HQC]2 TAP MOT

NHA X U A T B A N H A N 6 I

TRAN VINH

THIET KE BAI GIANG

HINH HOC 12 TAPMOT

NHA XUAT BAN HA NOI

LCll NOI DAU

Chifcfng trinh thay sach gan lien vdi viec do! moi phiidng phap day hoc,

trong do c6 viec thifc hien ddi mcfi pbifdng phap day hoc trong mon Toan.

Bo sach Thiei kebdi gidng Hinh hpc 12 ra dcrt de phuc vu viec ddi mcfi do.

Bp sacb difdc bien scan difa tren cac chifcfng, muc cua bo sach giao khoa

(SGK), bam sat noi dung SGK, tii do hinh thanh nen cau tnic mot bai giang theo

chifcfng trinh mdi difcfc viet theo quan diem boat dong va muc tieu giang day la:

Lay hoc sinh lam trung tam va tich cifc suf dung cac phifcfng tien day hoc hien dai.

Phan Hinh hoc gom 2 tap.

Tap 1: gom cac chifcfng I va mot phan chifcfng II

Tdp 2 : gom phan con lai cua Chifcfng II va chifcfng III

Trong moi bai scan, tac gia co 6\ia ra cac cau hoi va tinh hudng thu vj. Ve

boat dong day va hoc, chiing toi cd gang chia lam 2 phan: Phan boat dong cua

giao viSn (GV) va pban boat dong cua hoc sinh (HS), cf moi phan c6 cac cau hoi

chi tiet va hifcfng dan tra ldi. Thifc hien xong moi boat dong, la da thifc hien xong

mpt dcfn vi kien thufc hoac cung cd dcfn vi kie'n thifc do. Sau m6i bai hpc chiing toi

CO difa vac phan cau hoi trac nghiem khach quan nham de hpc sinh tif danh gia

difcfc miifc dp nhan thifc va mifc dp tiep thu kien thufc cua minh. Phan hinh ve, cac

tac gia cd gang sifu tam nhifng hinh anh thifc te co gan lien vdi lich suf toan hpc

trong chifcfng trinh Hinh hpc 12 nhif cac hinh da dien deu, ...Day la nhuhg hinh

ma khi iing dung trong bai giang se gay nhieu hiing thii trong hpc tap cua hpc sinh.

Day la bp sach bay, dufcfc tap the tac gia bien soan cong phu, lihg dung mpt

sd thanh tifU khoa hpc nhat dinb trong tinh toan va day hpc. Chiing toi hy vpng

dap ufng difcfc nhu cau cua giao vi6n toan trong viec ddi mdi phifcfng phap day hpc.

Trong qua trinb bien soan, khong the tranh khoi nhOhg sai sot, mong ban

dpc ram thong va chia se. Chiing toi chan thanh cam cfn sif gop y cua cac ban.

Hd Noi thdng 7 ndm 2008

Tac gia

ChirONq 1

KHOI DA mix

Phan 1

Gidl THltu CHLfdNG

I. CAU TAO CHUDNG

§1. Khdi niem \6 khdi da didn

§2 Khdi da dien Idi va khdi da dien deu

§3. Khai nidm ve the tich khdi da dien

On tap chuong I

Muc dich cua chuong

• Chuong I nham cung ca'p cho hoc sinh nhCing kie'n thiic co ban v6 khai niem cac khdi da di6n trong kh6ng gian, chu yeu la cac da dien Idi:

Khdi da dien, khdi chop.

Khai ni6m ve hinh da dien, khdi da dien.

Hai da dien bang nhau la gi ?

- Cac chia va ghep cac khdi da dien.

• Gidi thi6u ve khdi da di6n ldi va khdi da di6n deu.

• The tfch ciia khdi da dien:

Khai niem v^ th^ tfch khdi da dien.

Khai ni6m va cong thiJc th^ tfch khdi da dien.

The tfch khdi lang tru.

Thi tfch khdi chop.

I I - MUC TIEU

1. Kie'n thurc

Nam duoc toan bo kie'n thiic co ban trong chuong da neu tren.

Hieu cac khai niem va tfnh chat ciia khdi da dien.

" Hieu ve each thiic xay dung the tfch mot sd khdi da dien.

Hi6u dugc khdi da dien ldi.

2. KT nang

Phan biet dugc khdi da dien.

Tfnh dugc the tfch cua hinh lang tru, hinh chdp.

- Chiing minh dugc hai mat phang vuong gdc.

3. Thai do

Hgc xong chuong nay hgc sinh se lien he dugc vdi nhi6u va'n de thuc te sinh dgng, lien he dugc vdi nhiing van de hinh hgc da hgc b Idp dudi, md ra mgt each nhin mdi ve hinh hgc. Tix 66, cac em cd the tu minh sang tao ra nhiing bai toan hoac nhirng dang toan mdi.

Ke't ludn

Khi hgc xong chuong nay hgc sinh can lam tdt cac bai tap trong sach giao khoa va lam dugc cac bai kiem tra trong chuong.

P h a u 2>

ckc BAI SOAN

§1. Khai niem khoi da dien

(tiet 1, 2, 3)

I. MUC Tif U

1. Kien thurc

HS nam dugc:

1. Khai niem khdi da di6n trong khdng gian.

2. Hiû va van dung tinh th^ tich khdi lang tru va khdi chop.

3. Khai niem \i hinh da di6n \h. khdi da diâ

2. Kl ndng

• Ve thanh thao cac khdi da difin don gian.

• van dung thanh thao mdt sd phep bi6i hinh : Ddi xumg tam, ddi xiing true.

• Phan chia va ghep thanh thao khdi da didn.

3. Th i do

• Lien h6 dugc vdi nhiû vah 6i thuc te trong khdng gian.

• Cd nhiû sang tao trong hinh hgc.

• Humg thu trong hgc tap, tfch cue phat huy tfnh ddc lap trong hgc tap.

n. CHUAN BI CUA G V VA H&

1. Chu^nbicua GV:

• Hinh ve 1.1 d^n 1.14.

• Thudc ke, pha'n mau,...

2. Chuan bj cua HS :

Dgc bai trudc d nha, cd the lien he cac phep bien hinh da hgc d ldp dudi.

in. PHAN PHOI THC5I LUONG

Bdi dugc chia thdnh 3 tie't:

Tie't 1: Tir dau de'n bet muc 1 phan II.

Tie't 2: Tie'p theo de'n bet phan III

Tie't 3: Tie'p theo den bet phan IV va phan bai tap

IV. TIEN TBlNH DAY HOC

n. f>^J VAN DC

Cau hdi 1.

Cau hoi 2.

Nhac lai khai niem hinh hop, hinh chdp.

Cho hinh hop ABCDA'B c u

a) Hay xac dinh cac mat cua hinh hop.

b) Hay xac dinh cac dinh va cac canh ciia hinh hop.

a. RM MOI

• Thuc hien A l trong 5 phiit.

Hoat dgng cua GV

Cdu hoi I

Nhac lai dinh nghia hinh lang tru.

Neu mgt sd vf du.

Cdu hoi 2

Nhac lai dinh nghla hinh chdp.

Neu mgt sd vi du.

Hoat dgng ciia HS

Ggi y trd loi cdu hoi I

HS tu neu.

Ggi ytrd loi cdu hoi 2

HS tu neu.

HOATDONCI

I. K H 6 I LANG TRU VA K H 6 I CHOP

GV neu cau hoi :

HI. Khdi rubic cd bao nhieu mat?

H2. Mdi mat ciia khdi rubic la hinh gi?

• GV six dung hinh 1.2 trong SGK va dat van d6:

H3. Hay dgc ten cac khdi chdp d hinh 1.2.

H4. Hay ke ten cac mat cua hinh 1.2.

H5. Hay ke ten cac mat day cua hinh 1.2

H6. Cac canh ben ciia hinh lang tru cd quan h6 vdi nhau nhu the nao?

H7. Neu mgt sd hinh anh thuc te ve hinh lang tru va hinh chdp.

nOATDONG2

n. KHAI NifiM Wt HINH DA DifiN VA KHOI DA D I £ N

1. Khai niem ve hinh da di n

Stt dung hinh 1.4

• Thuc hien A 2 trong 4 phut.

Hoat dong ciia GV

Cdu hoi I

Hay ke ten mat day ciia hinh lang

tm ABCDE.A'B'C'D'E'

Cdu hoi 2

Hay k^ ten mat day ciia hinh

chdp S.ABCDE.

Hoat dpng cua HS

Ggi y trd l&i cdu hoi I

Do la cac hinh da giac

ABODE va A'B'C'D'E'

Ggi y trd loi cdu hoi 2

Do la hinh da giac ABODE.

• GV dat cac cau hoi sau :

H8. Trong hinh 1.4 hinh lang tru cd nhOng da giac nao?

H9. Trong hinh 1.4 hinh chdp cd nhung da giac nao?

HIO. Cac da giac cua cac hinh tren quan he vdi nhau nhu the nao?

• GV neu tfnh chat:

a) Hai da gidc phdn biet chi cd the : Hoac khdng cd diem chung hoac cd

mdt cgnh chung.

b) Mdi cgnh ciia da gidc ndo cUng Id cgnh chung cOa dUng hai da gidc.

• GV n6u dinh nghia hinh da dien:

Hinh da dien Id hinh dugc tgo bdi cdc da gidc thda mdn 2 tinh chdt tren.

Hll . Hay ndu mdt sd vf du v^ hinh da didn.

HI2. Hay k^ ten hinh da diSn cd cac da giac bang nhau.

H14. Trong hinh 1.5 em hay k^ tdn cac day ciia hinh da didn.

2. Khai niem ve khdi da di n

• GV ndu dinh nghla :

Khdi da dien Id phdn khdng gian dugc gidi hgn bdi hinh da dien, ke cd hinh da dien dd.

• GV cd th^ lay mdt hinh da didn, bo bdt di mdt sd mat va hoi:

H15. Hinh viia nhan dugc cd phai khdi da didn hay khdng?

• GV ndu cac khai nidm :

HI6. Di^m trong ciia khdi da didn la gi?

HI7. Di^m ngoai cua khdi da didn la gi?

H18. Cd di m nao khdng la di m trong cung khdng la di^m ngoai ciia khdi da didn.

H19. Mi6n trong ciia khdi da didn la gi?

H20. Mien ngoai ciia khdi da didn la gi?

H21 .Mdt dudng thang cd th^ nam trgn d mi^n nao ciia khdi da didn?

H22. Hay ke tdn mdt sd hinh khdng phai la khdi da didn.

10

• Thuc hidn ^ 3 trong 4 phiit.

Hoat dgng ciia GV

Cdu hoi I

Hinh 1.8c cd vi pham tfnh chat

nao khdng ?

Cdu hoi 2

Giai thfch vi sao hinh 18c khdng

phai la khdi da dien

Hoat ddng ciia HS

Ggi y trd loi cdu hoi I

Vi pham tfnh chat a.

ABODE va A'B'C'D'E'

Ggi y trd led cdu hoi 2

GV cho HS phat biû va kdt luAn.

HOATDONC 3

HL HAI DA DifeN BANG NHAU

1. Phep ddi hinh trong khong gian

• GV ndu dinh nghia:

Trong khdng gian, quy tdc dgt tuang Ang mdi diem M vdi duy nhdt mat

diem M' dugc ggi Id phep bie'n hinh trong khdng gian.

Phep bien hinh trong khdng gian la phep ddi hinh neu nd bdo todn khodng cdch.

• GV ndu mdt sd phep ddi hinh thudng gap trong khdng gian.

a) Phep tinh tien theo vecta v

Phep tinh tien theo vecta v Id phep bien hinh bien M thdnh M' md

MM' = v

H22. Hay chiing minh phep tinh tien theo vecto v la phep ddi hinh.

b) Phep ddi xicng qua mat phdng (P)

• GV sit dung hinh 1.10b va ndu khai nidm:

11

Phep dd'i xiing qua mat phdng (P) la phep bien hinh bie'n mdi diem thudc

(P) thdnh chinh nd. Bie'n mdi diem M khdng thugc (P) thdnh M' md (P) la

mat phdng trung trUc ciia MM'.

H23. Hay chiing minh phep ddi xiing qua mat phang (P) la phep ddi hinh.

c) Phep ddi xdng tdm O

GV sit dung hinh 1.1 la va ndu khai niem:

Phep ddi xdng tdm O la phep biin hinh bie'n O thdnh chinh nd. Bien mdi

diem M khdc O thdnh M' md O la trung diem cua MM'

H24. Hay chiing minh phep ddi xiing tam O la phep ddi hinh.

d) Phep ddi xiing qua dudng thdng A

GV sii dung hinh 1.1 la va neu khai niem:

Phep dd'i xdng qua dudng thdng A la phep bien hinh bien mdi diem thudc

A thdnh chinh nd. Biin mdi diem M khdng thudc A thdnh diem M' md A

la dudng trung true cua MM'.

H25. Hay chung minh phep ddi xiing qua dudng thang A la phep ddi hinh.

• GV neu nhan xet:

Thuc hien lien tie'p cdc phep ddi hinh ta dugc phep ddi hinh.

Phep ddi hinh biin da dien (H) thdnh da dien (H') vd dinh, cgnh, mat

cua (H) thdnh dinh, cgnh, mat cua (H').

2. Hai hinh bang nhau

• GV ndu dinh nghla:

Hai hinh dugc ggi Id bdng nhau neu nd cd mdt phep ddi hinh bie'n hinh

ndy thdnh hinh kia.

GV su dung hinh 1.12 de md ta dinh nghia tren.

• Thuc hien A 4 trong 4 phiit.

12

B'

A'

Hoat dgng ciia GV

Cdu hoi I

Ggi 0 la tam cua hinh hop. Phep

ddi xiing tam 0 bien hinh lang tru

ABD.A'B'D' thanh hinh nao ?

Cdu hoi 2

Chiing minh hai hinh hop tren

bang nhau.

Cdu hoi 3

Hay tim mgt phep bie'n hinh khac bie'n

ABD.A'B'D thanh hinh CDB.C'B'D'

Hoat dgng ciia HS

Ggi y trd ldi cdu hoi I

ABD.A'B'D' thanh hinh CDB.C'B'D'

Ggi y trd ldi cdu hoi 2

HS tu chiing minh.


HS tu tim.

nOATDONG 4

IV. PHAN CHIA VA LAP GHEP CAC KHOI DA D I £ N

• GV neu each chia mdt sd khdi da dien va dat cau hdi:

H26. Khi nao cd the chia mgt khdi da dien thanh hai khdi da dien khac nhau?

H27. Hinh hop chii nhat cd the chia dugc thanh hai khdi da dien hay khdng? hay neu each chia va ke ten cac khdi da dien tao thanh.

• GV neu nhan xet:

Mdt khdi da didn bat ki cd the chia thanh cac khdi da dien.

13

HOATDONG^

TbM TflT Bfll HQC

1. a) Hai da giac phan bidt chi cd th^ : Hoac khdng cd diem chung hoac cd mdt

canh chung.

b) Mdi canh ciia da giac nao ciing la canh chung ciia diing hai da giac.

2. Hinh da didn la hinh dugc tao bdi cac da giac thda man 2 tfnh cha't trdn.

Khdi da didn la ph^ khdng gian dugc gidi han bdi hinh da didn, ke ca hinh da

didn dd.

3. Trong khdng gian, quy tac dat tuong iing mdi didm M vdi duy nha't mdt diem

M' dugc ggi la phep bid'n hinh trong khdng gian.

Phep bie'n hinh trong khdng gian la phep ddi hinh neu nd bao toan khoang each.

4. Phep tinh tid'n theo vecto v la phep bie'n hinh bid'n M thanh M' ma MM' = v.

5. Phep ddi xumg tam O la phep bid'n hinh bid'n O thanh chfnh nd. Bid'n mdi diem

M khac O thanh M' ma O la trung diem ciia MM'

6. Ph6p ddi xumg qua dudng thang A la phep bid'n hinh bidn mdi diem thudc A

thanh chfnh nd. Bidn mdi didm M khdng thudc A thanh diem M' ma A la dudng

trung true ciia MM'

7. Thuc hidn lidn tidp cac phep ddi hinh ta dugc phep ddi hinh.

Phep ddi hinh bien da didn (H) thanh da didn (H') va dinh, canh, mat cua (H)

thanh dinh, canh, mat ciia (H').

8. Hai hinh dugc ggi la bang nhau nd'u nd cd mdt phep ddi hinh bidn hinh nay

thanh hinh kia.

14

HOATDQNG 6

MOT S6 CflU H 6 | TRflC NGHIpM

Hay dien diing (D) sai (S) vao cac khang dinh sau :

Cdul. Cho hmh hdp ABCDEFGH

B

(a) Hinh hop trdn la mdt khdi da didn

(b) Cd the chia hinh hop trdn thanh hai lang tru bang nhau

(c) Tdn tai phep ddi xiing tam O bid'n cac dinh cua hinh hop

thanh cac dinh ciia nd

(d) Ca ba khang dinh trdn ddu sai

Trd ldi.

a

D

b

D

c

D

d

S

D •

D D

Cdu 2. Cho hinh hdp ABCD.A'B'CD'. Ggi O la tam ciia hinh hdp, phep ddi xiing

tam D(o)

15

B' C

A' y^ 1 "•

B: . - ' \

**• • .

^.^^

D'

(a)D(0)(A) = C'

(b)D(0)(B) = B'

(c )D(0) (B)-D '

(d)D(0)(A) = C.

Trd ldi.

D

D 1

D D

a

D

b

S

c

D

d

S

Cdu 3. Cho hinh hop ABCD.A'B'CD'. Ggi O la tam ciia hinh hop, phep ddi xiing

tam D, '(O) B'

A' y 1 N

1 ^ ^ ' ' '

B

yy \ - -y^'

f j r

D'

(a) D(0)(BAC.B'A'C') = DAC.D'A'C'

(b) D(0)(ABD.A'B'D') = CBD.C'B'D'

(c) D(0)(ABCD.A'B'C'D') = ABCD.A'B'C'D'

(d) Ca ba khang dinh tren deu sai.

16

D

D

D

D

Trd ldi.

a

D

b

D

c

D

d

S

Cdu 4. Cho hinh chdp ddu S.ABCD (hinh ve)

A B

(a) Hai hinh chdp S.DOA va S.BOA bang nhau

(b) Hai hinh chdp S.DOC va S.BOC bang nhau

(c) Hai hinh chdp S.BOA va S.BOC bang nhau

(d) Ca ba khang dinh tren deu sai

Trd ldi.

a

D

b

D

c

D

d

S

• • D D

Chgn khang dinh diing trong cac cau sau:

Cdu 5. Cho hinh chdp deu S.ABCD (hinh ve). Qua phep ddi xiing qua mat phang (SDB) bie'n hinh chdp S.AOB thanh hinh chdp

17

(a) S.DOA ;

(c) S.COB;

Trd ldi. (c).

(b) S.DOC

(d) S.DBC

Cdu 6. Cho hinh chdp deu S.ABCD (hinh ve). Qua phep ddi ximg qua mat phang

(SDB) bie'n hinh chdp S.DAB thanh hinh chdp

(a) S.DOA ;

(c) S.COB;

Trdldi. (d).

(b) S.DOC

(d) S.DBC

18

Cdu 7 Cho hinh chdp deu S.ABCD (hinh ve). Qua phep ddi xirng qua mat phang

(SAC) bie'n hinh chdp S.DAB thanh hinh chop

(a) SDOA ; (b) S.DOC

(c) S.COB i (d) S.DAB

Trdldi. (d).

Cdu 8. Cho hinh chdp ddu S.ABCD (hinh ve). Qua phep ddi xiing qua mat phang

(SAC) bie'n hinh chdp S.OAB thanh hinh chdp

(a) S.DOA;

(c) SCOB;

Trdldi. (a).

(b) S.DOC

(d) S.DAB

19

Cdu 9. Cho hinh chdp deu S.ABCD (hinh ve). Qua phep ddi xung tam O bie'n hinh

chop S.OAB thanh hinh chdp

(a) S.DOA; s' (b) S.DOC

(c) S.AOB ; (d) S.DOC

Trd ldi. (d).

Cdu 10. Cho hinh chdp deu S.ABCD (hinh ve). Qua phep ddi xiing tam O bie'n

hinh chdp S.ABCA thanh hinh chdp

20

(a) S.DOA ;

(c) S.AOB;

Trd ldi. (b).

(b) S'.ABCD

(d) S.DAB

HOATDQNG 7

HaOTNG DflN Bfll TflP SGK

Bai 1. Hudng ddn. Dua vao tinh chat ciia da dien

Hai mat kd nhau ludn cd mgt canh chung

Mdi canh cua da dien la canh chung cua hai mat.

Hoat dgng cua GV

Cdu hoi I

Gia sii da dien cd n mat, cac mat khdng cd canh chung thi cd tat ca bao nhieu canh ?

Cdu hoi 2

Mdi canh ciia da dien la canh chung ciia 2 mat nen sd mat la bao nhieu ?

Cdu hoi 3

Nhan xet vdsd mat.

Cdu hoi 4

Neu vf du.

Hoat dgng cua HS


Cd tat ca 3n canh.


Co tat ca — mat. 2 •


Sd mat phai cbSn.


HS tu lay vi du.

Bai 2. Hudng ddn. Dua vao tfnh chat ciia da dien

Dinh cd k mat di qua thi cd k canh di qua.

Mdi dinh cd it nhat la 3 mat di qua.

21

Hoat dgng cua GV

Cdu hoi 1

Mdi canh cua da dien di qua ma'y dinh.

Cdu hoi 2

Tdng sd canh so vdi tdng sd mat nhu the nao?

Cdu hoi 3

Sd mat di qua mgt dinh la chan

hay le ?

Cdu hoi 4

Sd dinh la chan hay le?

Hoat dgng ciia HS


Mdi canh ciia tii dien di qua dung 2 dinh.


Tdng sd canh bang 2 lan tdng sd mat.

Gai y trd ldi cdu hoi 3

La sd le.


Sd dinh phai la so chan.

HS tu neu vf du.

Bai 3. Hifdng ddn. Dua vao tfnh cha't ciia da dien va hinh lap phuong.

Hinh lap phuong cd 8 dinh va 6 mat.

Sd canh cua hinh lap phuong la 12.

G

Hoat dgng cua GV t

Cdu hoi I

Hay ke ten 5 hinh tii dien d hinh tren.

Cdu hoi 2

Cdn each chia nao khac khdng?

Cdu hoi 3

Hay neu mgt each chia khac.

Hoat dgng cua HS

Gg-' y trd ldi cdu hoi I

HS tu tra Idi.


van cdn nhidu each chia khac niia.


HS tur tra ldi

22

Bai 4. Hudng ddn. Dua vao tfnh chat ciia da dien va hinh lap phuong.

Hinh lap phuang cd 8 dinh va 6 mat.

Sd canh ciia hinh lap phuong la 12.

F • G -

/ ' j \ D ^ l - . ^ B / V ^ ' /-•

y s A

/

H

D

Hoat dgng ciia GV

Cdu hdi I

Hay kd ten 6 hinh tii dien d hinh tren.

Cdu hoi 2

Cdn each chia nao khac khdng?

Cdu hoi 3

Hay neu mdt each chia khac.

Hoat dgng cua HS


HS tu tra ldi.


Van cdn nhidu each chia khac niia


HS tu neu.

23

§2. Khoi da dien loi va khoi da dien deu (tiet 4, 5)

I. MUC TIEU

1. Kie'n thurc

HS nam dugc:

1. Dinh nghia khdi da dien ldi, phan biet dugc khdi da dien loi va khdi da dien deu.

2. Nam dugc dinh nghia khdi da dien ddu.

3. Hieu rd tfnh chat ciia khdi da dien deu.

4. Nhan bie't dugc mdt so khdi da dien ddu.

2. KT nang

• Bie't phan biet da dien ldi va da dien khdng ldi.

• Bie't dugc mgt sd da dien ddu va chiing minh dugc mdt da dien la d:i dien ddu.

3. Thai do

Lien he dugc vdi nhidu van dd cd trong thuc te vd hai dudng thang vudng gdc.

Cd nhidu sang tao trong hinh hgc.

Hiing thii trong hgc tap, tich cue phat huy tfnh ddc lap trong hgc tap.

II. CHUAN 51 CUA GV VA HS

1. Chuan bi ciia GV:

• Hinh ve 1.17 den 1.22 trong SGK.

• Thudc ke, pha'n mau,...

• Chuan bi san mgt vai hinh anh thuc te trong trudng vd hai dudng thang vudng gdc nhu: cac dudng thang cua tudng,...

2. Chuan bj ciia HS :

• Dgc bai trudc d nha, dn tap lai mdt sd tfnh cha't hinh chdp va hinh tru.

• Chudn bi thudc ke, biit chi, biit mau dd ve hinh.

24

in. PHAN PHOI TH6I LUONG

Bai nay chia thanh 2 tiet:

Tie't 1: Tit dau de'n bet dinh nghia phan II.

Tiet 2 : Phan cdn lai va hudng dan bai tap.

IV. TIEN TDINH DAY HOC

n. DRT Vn'N D€

Cau hoi 1.

Cho hinh chdp S.ABCD. Day la hinh vudng.

a) Ne'u SA vudng gdc vdi day thi cac mat ben cd quan he nhu te' nao?

b) SA vudng gdc vdi day nhung day ABCD la hinh binh hanh thi cac mat ben cd quan he nhu the nao?

Cau hoi 2.

Neu mdt sd tfnh cha't co ban ciia hinh da dien.

a. am AA6I

HOATDQNGl

I. KHOI DA DifeN LOI

GV sit dung hinh 1.17 (nen dat ten cac dinh va cac diem) va neu van dd :

25

a) ^ b) HI. Em cd nhan xet gi vd doan thang EF trong hinh a)?

H2. Em cd nhan xet gi vd doan thang MN trong hinh b)?

GV nen lay mdt khdi da didn khdng Idi de so sanh.

Tren hinh ve M e mp(EFF'E), N e mp(DEE'D').

H3. MN cd nam trgn trong hinh lang tru dd khdng?

• GV neu dinh nghla trong SGK

Khdi da dien (H) dugc ggi Id khdi da dien ldi ne'u mdt dogn thdng ndi hai

diem bdt ki thudc (H) deu ndm trgn trong (H).

H4. Hay ndu mgt sd vf du vd khdi da dien ldi.

26

»Thuc bien Al trong 5 phiit.

Hoat dgng cua GV

Cdu hoi I

Hay neu vf du vd khdi da dien ldi

trong thuc te.

Cdu hoi 2

Hay neu vi du vd khdi da dien

khdng ldi trong thuc te.

Cdu hoi 3

Neu su khac nhau giiia da dien

ldi va da dien khdng ldi.

B

Hoat dgng cua HS


Hinh lap phuong (hop phan), hinh hop

chii nhat...


HS tu neu vi du bang dung cu thuc

te,...


HS tu tra Idi.

HOATDQNG 2

H. KHOI DA DifiN D £ U

• GV sit dung hinh 1.19 va neu cau hdi:

H5. Hinh lap phuong cd tfnh chat chung gi ve cac mat?

H6. Tii dien ddu cd tinh chat chung gi vd cac mat?

27

GV neu dinh nghia :

Khdi da dien diu Id khdi da dien ldi cd tinh chdt sau:

a) Mdi mat cua nd Id mot da gidc diu p cgnh.

b) Mdi dinh cua nd Id dinh chung cua diing q mat.

Khd'i da dien deu nhu vdy ngUdi ta ggi Id khd'i da dien diu logi {p, qj.

H7. Mdi mat ciia khdi da dien ddu la nhiing da giac ddu bang nhau. Diing hay sai?

H8. Cd ngii giac ddu khdng?

• GV neu dinh II:

Chi cd ndm logi da dien deu (3, 3), (4, 3), (3, 4), {5, 3} vd {3, 5).

H8. Hay ve khdi da dien ddu {4, 3} va {3, 4}.

• GV gidi thieu mdt sd hinh anh vd da giac ddu ciia Le-d -na Do Vin -ci

a) b)

Kiioi da dien 12 mdt

28

: ^ ^

a) b)

Khd'i da dien deu 20 mat

• Thuc hien ^ 2 trong 5 phiit.

Hay cho HS tu ve bat dien ddu.

Hoat dgng cua GV

Cdu hoi 1

Hay de'm cac dinh cua bat dien ddu.

Hoat dgng cua HS


Gdm 6 dinh

29

Cdu hoi 2

Hay dem cac canh ciia bat dien

ddu.


12 canh.

• GV cho HS didn vao bang tdm tat sau:

Loai

{3,3}

{4,3}

{3,4}

{5,3}

{3,5}

Ten goi So dinh So canh So mat

• Thuc hien vi du 1 trong 15'

cau a. Su dung hinh 1.22 a trong SGK.

Hoat dgng cua GV

Cdu hoi I

Hay ve hinh va dat ten cho cac dinh cua bat dien.

Cdu hdi 2

Ke ten cac mat cua bat dien.

Hoat dgng cua HS


HS tu ve hinh va dat ten.


HS tu liet ke toan bg

Thuc hien ^ 3 trong 5 phiit

30

Hoat dgng ciia GV

Cdu hoi I

Hay chi ra mdt sd mat ciia bat dien.

Cdu hoi 2

Chiing minh cac mat ciia bat dien la cac tam giac ddu

Hoat dgng cua HS


HS tu chi ra.


Tam giac NEJ ching ban ta thay day

la tam giac ddu canh —

cau b. Sii dung hinh 1.22 b trong SGK.

Hoat dgng cua GV

Cdu hoi I

Hay ve hinh va dat ten cho cac dinh ciia bat dien.

Cdu hoi 2

Ke ten cac mat ciia bat dien.

Hoat dgng cua HS

Gen y trd ldi cdu hoi 1

HS tu ve hinh va dat ten.


HS tu liet ke toan bd

Thuc hien ^ 4 trong 5 phiit.

31

A'

Hoat dgng ciia GV

Cdu hoi I

Hay chi ra mgt sd mat ciia bat

dien.

Cdu hoi 2

Chiing minh cac mat ciia bat dien

la cac tam giac ddu.

Hoat dgng ciia HS


HS tu chi ra.


Tam giac NEJ chang ban ta thay day

la tam giac ddu canh —

HOATDQNG 3

TdM TflT Bfll HPC

1. Khdi da dien (H) dugc ggi la khdi da dien ldi ndu mdt doan thang ndi hai diem bat ki thudc (H) ddu nam trgn trong (H).

2. Khdi da dien ddu la khdi da dien Idi cd tfnh chat sau:

a) Mdi mat cua nd la mdt da giac ddu p canh.

b) Mdi dinh cua nd la dinh chung ciia diing q mat.

Khdi da dien ddu nhu vay ngudi ta ggi la khdi da didn ddu loai (p, q}.

32

3. Chi cd nam loai da dien ddu {3,3}, {4,3}, {3,4}, {5,3} va {3,5}.

HOAT DONG 4

MQT SO CflU HOI TRflC NGHIEM

Cdu I. Hay didn diing, sai vao cac d trdng sau day:

Cho hinh tur dien :

(a) Hinh tii dien cd 4 dinh

(b) Hinh tii dien cd 4 mat

(c) Hinh tii dien cd 4 canh

(d) Cac mat la nhiing tam giac

Trd ldi.

a

D

b

D

c

S

d

D

n D D

Cdu 2 Hay didn diing, sai vao cac d trdng sau day:

33

Cho hinh ve

(a) Cd mdt hinh bat dien cua hinh tren

(b) Hinh bat dien cd mdt mat la hinh vudng

(c) Hinh bat dien cd tat ca cac mat la cac tam giac

(d) Hinh bat dien dd cd the la hinh bat dien ldi

Trd ldi.

a

D

b

S

c

D

d

D

Chgn cdu trd ldi ddng trong cdc bdi tap sau:

.Cdu 3 Cho hinh ve:

D D D D

34

- - r C

(a) Hinh da cho la mdt khdi da dien ldi

(b) Hinh tren khdng the la khdi da dien Idi.

(c) Cac mat cua khdi da dien tren la nhiing tam giac

(d) Ca ba cau trdn deu sai.

Trd ldi (a).

Cdu 4. Cho hinh hop chii nhat ABCDA'B'CD'

D'

(a) Cac mat ciia hinh hop la hinh vudng.

(b) Cac mat ciia hinh hop la hinh tam giac.

(c) Cac mat ciia hinh hop la hinh chii nhat.

(d) Cac mat cua hinh hop la hinh thoi.

Trd ldi (c).

Cdu 5 Cho hinh chop ddu ABCD. Gdc ADB bang

D

(a) 60°; (b) 120°;

(c) 90"; (d) 150°

Trd ldi (a).

Cdu 6. Cho tii dien deu ABCD. Tdng ba gdc d dinh A la

(a) 90° (b)180°

(c) 45° (d) 30°

Trdldi (b).

Cdu 7. Cho mdt bat dien ddu. Mdi gdc tai mdt dinh cua mdt mat la

(a) 90° (b) 60°

(c) 45° (d) 30°

Trd ldi (b).

HOAT DONG 6

mtftiQ DflN GIfll Bfll TAP SflCH GIflO KHOfl

Bai 1. Day la bai tap thuc hanh. GV yeu cau HS ga'p giay va thuc hien.

36

/ ' ^

/ B

/ A

/

D

b)

GV dat cac cau hdi sau :

c)

Hoat ddng cua GV

Cdu hoi 1

0 hinh thii nhat sau khi cat va gap

ta dugc hinh gi?

Cdu hoi 2

0 hinh thii hai sau khi cat va ga'p

ta dugc hinh gi?

Cdu hoi 3

6 hinh thii ba sau khi cat va ga'p

ta dugc hinh gi?

Hoat dgng cua HS


Hinh tii dien deu, hinh a)


Hinh lap phuong, hinh b).


Hinh bat dien ddu, hinh c).

Bai 2. Sit dung vf du 1.

37

Hoat dgng cua GV

Cdu hoi I

Ggi canh ciia hinh lap phuong la a.

IMi dien tich toan i^hin cua hinh (H).

Cdu hdi 2

Hay tinh canh cua hinh bat dien.

Cdu hdi 3

Tinh dien tfch toan phan ciia hlnh

(H').

Cdu hdi 4

Tfnh ti sd dien tfch toan phan cua

hinh(H)va (H').

Hoat ddng ciia HS


S = 6al


aV2 Canh cua hinh bat dien la

2 Ggi y trd ldi cdu hoi 3

S'= a^Vs.


^ = 2V3 S'

Bai 3. Sii dung tinh chat cua tii dien ddu.

38

Hoat ddng cua GV

Cdu hdi I

Ggi canh ciia hinh tii dien ddu la

a. Tfnh canh ciia hinh MNEF

Cdu hoi 2

Chiing minh • MNEF la hinh tir

dien ddu.

Hoat dgng cua HS

Ggi y trd ldi cdu hdi I

NM = -3


Chiing minh cac canh bang nhau.

Bai 4. Sit dung tinh chat cua bat dien ddu.

39

Cau a)

Hoat dgng cua GV

Cdu hoi 1

Chiing minh B, C, D, E thudc mat

phing trung true cua AF.

Cdu hdi 2

Hay chifng minh EC, BD va AF

ddng quy.

Cdu hdi 3

Chung minh cau a).

Hoat ddng ciia HS

Ggi y trd ldi cdu hdi 1

HS tu chiing minh.


Ta tha'y BODE la hinh thoi nen BD va CE

cat nhau tai trung diem I ciia mdi dudng.

ABFD ciing la hinh thoi nen AF va

BD ciing cit nhau tai trung diem I.


HS tur chiing minh.

caub)

Hoat dgng cua GV

Cdu hdi I

Chiing minh ABFD la hinh vudng.

Cdu hdi 2

Chiing minh cau b).

Hoat ddng cua HS


HS tu chiing minh AF = BD Tuf dd

ta cd ABFD la hinh thoi cd hai dudng

cheo bang nhau.


HS tu chiing minh.

40

§3. Khai niem the tich cua khoi da dien

(tiet 6, 7, 8)

1. MUC Tl£u

I. Kien thufc

HS nam dugc:

1. Khai niem the tfch cua khdi da dien.

2. Cac cdng thiic tinh the tfch ciia mdt sd khdi da dien cu the.

3. Tinh chat va the tfch ciia khdi lang tru, khdi chdp.

2. KI nang

• Tfnh dugc the tfch hinh lang tru, hinh chdp.

• Tfnh dugc ti sd the tfch cac khdi da dien dugc tach ra tix mdt khdi da dien.

3. Thai do

• Lien he dugc vdi nhidu va'n dd cd trong thuc te vd khdi da dien.

• Cd nhidu sang tao trong hinh hgc.

• Hiing thii trong hgc tap, tfch cue phat huy tfnh ddc lap trong hgc tap.

n. CHUAN BI CUA GV VA m

1. Chuan bi cua GV:

• Hinh ve 1.256 den 1.28 trong SGK.

• Thudc ke, phah mau,...

• Chu^ bi san mdt vai hinh anh thuc te vd khdi da didn.

2. Chuan bj cua HS

Dgc bai trudc d nha, dn tap lai mgt sd tfnh chat ciia khdi lang tru, khdi chdp.

41

in. PHAN PHOI THCbl LUONG

Bai nay chia thanh 3 tiet:

Tie't 1 : Tii dau de'n bet phan I.

Tiet 2 : Phin II.

Tie't 3 : Phan III

IV. TIEN TPINH DAY HOC

n. t)RT vnN f>€

Cau hdi 1.

Neu cdng thiic tfnh the tich mdt sd hinh ma em da hgc

Cau hdi 2.

Thd tfch hinh lap phucmg canh bang a la bao nhieu ?

Cau hoi 3.

Hai hinh lap phuong bang nhau thi the tfch bang nhau. Diing hay sai?

Cau hdi 4.

Em cd nhan xet nhiing hinh nhu the nao thi cd thd tfch.

0. sni M 6 I

HOATDQNGl

I . KHAI NifiM Nt THfi TICH KHOI DA DifeN

• GV dat ra mdt sd tinh hudng:

HI. Hinh lap phuong cd canh bing 1 thi the tfch la bao nhieu?

H2. Hai khdi da dien bing nhau lieu thd tfch cd bing nhau khdng?

H3. Neu khdi da dien dugc phan chia thanh hai khdi da dien thi quan he the tfch giiia chiing nhu the nao ?

42

GV dua ra ba md hinh the hien cho ba y tren bing hinh anh sau:

----^ z:===-

1 J- - -

y^\""-

1 , -,5,-5.'^'*' '~'

r<r^

- - " ~^^^^^^x^

__.-— a)

~v o

'tmr:.

c)

Hinh a): Hinh lap phuong canh la 1 cd the tfch la 1.

Hinh b) Hai khdi da dien qua phep ddi xiing tam O bing nhau cd the tfch bing nhau.

Hinh c): Hinh bat dien ddu dugc tach ra thanh hai hinh chdp.

• GV ndu ke't luan:

a) Neu (H) la khdi lap phuang cd cgnh Id 1 thi N,^^^ = 1.

b) Ne'u (H) = (H) thi V(j ) = V(H.)

c) Neu (H) dugc phdn chia thdnh hai khd'i da dien (H,) vd (H2) thi

V(H)=V,)+>2)

Sd duang V,^^^ ndi tren dugc ggi Id the tich ciia khd'i da dien (H).

The tich khdi lap phuang cd cgnh la 1 ggi la khdi lap phuang dan vi.

43

• GV neu vf du, phan tfch cac hinh d hinh 1.25 va ndu cac cau hdi:

H4. Khdi da dien nao la khdi lap phuong don vi?

H5. Lieu mgi khdi da dien cd the tfnh the tfch qua khdi lap phuong don vi dugc

hay khdng?


(Ho)

Hoat dgng cua GV

Cdu hoi 1

Trong hinh (H,) cd bao nhieu

hinh lap phuong ?

Cdu hdi 2

Trong hinh (Hi) cd bao nhieu

hinh (Ho).

Cdu hdi 3

Tfnh V(j ) theo V^^ )

(H,)

Hoat dgng ciia HS


5 hinh lap phuong.


Cd 5 hinh (H^).


> , ) = 5 > . ) GV ndu ke't luan :

Ggi (H,) Id khd'i hop chii nhdt kich thdc a = 5,b = l,c = l.

Thuc hien A 2 trong 3 phiit.

/

^ / / / / / / / / /

/ / / / / / / / / /

/ /

(H,) (Ha)

44

Hoat ddng cua GV

Cdu hdi I

Trong hinh (H2) cd bao nhieu hinh (H,) ?

Cdu hdi 2

Trong hinh (H2) cd bao nhieu hinh (Ho).

Cdu hdi 3

Tinh V(jj^) theo V(H^).

Hoat ddng ciia HS


4 hinh lap phuong.


Cd 20 hinh (Ho).


> . ) = " • > , )

• GV neu ke't luan :

Ggi (H2) Id khdi hop chii nhdt kich thdc a = 5,b = 4,c = 1.


/

/^ / / / /

/ y / / / / / / /

/

/

v

X / y / / / / / / /

/ / / / / / / / / /

/

/

/ /

/

/

V (Hj)

Hoat dgng cua GV

Cdu hdi 1

Trong hinh (H) cd bao nhieu hinh (H^)?

Cdu hdi 2

Trong hinh (H) cd bao nhieu hinh

(Ho)?

Cdu hdi 3

Tinh V(H) theo V(H^).

(H)

Hoat dgng cua HS


4 hinh (Hj).


Cd 60 hinh (Ho).


V(H)-3.V(H^)

45

• GV neu ke't luan :

Ggi (H) la khdi hop chu nhdt kich thudc a = 5,b = 4,c = 3.

• GV ke't luan :

V(H)= a.b.c

• GV neu dinh If:

The tich ciia khdi hop chit nhdt bdng tich cua ba kich thudc.

• Mdt so cau hdi ciing cd :

H6. Hinh hop cd kfch thudc 1, 2, 3 cd the tfch la 6.

(a) Dung (b) Sai.


(a) Diing (b) Sai.


(a) Diing (b) Sai.


(a) Diing (b) Sai.

HIO. Hinh hop cd kfch thudc - , 2, 3 cd thd tfch la 3.

(a) Diing (b) Sai.

3 H l l . Hinh hop cd kfch thudc 1,2, — cd the tfch la 3.

(a) Diing (b) Sai.

HI2. Hinh hdp cd kfch thudc 1, - . 3 cd thd tfch la 1. 3

(a) Dung (b) Sai.

46

HOATDQNG 2

H. THE TICH KHOI LANG TRU

H12. Hinh hop chii nhat cd phai la hinh lang tru khdng?

H13. Hay tfnh dien tfch day S cua hinh (H).

H14. Hay tfnh chidu cao h ciia hinh (H).

HI5. Hay tfnh Sh.

Hld.^So sanh thd tfch ciia (H) va S.h.

• GV neu van dd : Ngoai nhung hinh dac biet nhu hinh hop chii nhat, mgi hinh

lang tni cd the tich nhu vay.

• GV neu dinh II:

The tich khdi ldng tru cd dien tich ddy B vd chieu cao h IdV = B.h.

• Mdt sd cau hdi ciing cd

H17. Hinh lang tru cd dien tfch day la 8 chidu cao 7 cd thd tfch la 56.

(a) Diing (b) Sai.

H18. Hinh lang tru cd dien tfch day la — chidu cao 8 cd the tfch la 4.

(a) Diing (b) Sai.

H19. Hinh lang tru cd dien tich day la 8 chidu cao — cd the tfch la 4.

(a) Diing (b) Sai.

3 H20. Hinh lang tru cd dien tfch day la 8 chieu cao — cd the tfch la 12.

(a) Dung (b) Sai.

47

HOATD(DNG3

III. THE TICH HINH CHOP

• GV neu dinh 11:

The tich khdi chdp cd dien tich ddy Id B, chieu cao h la

V = -B.h. 3


Hoat dgng cua GV

Cdu hdi 1

Tfnh dien tfch day ciia Kim tu

thap.

Cdu hdi 2

Tfnh the tfch khdi chdp Kim tu

thap.

Hoat ddng cua HS


B = 230.230= 113400 m'


V = -.113400. 147 401200m' 3

• Thuc hien vf du trong 5'. Sit dung hinh 1.28 trong SGK.

cau a.

Hoat ddng cua GV

Cdu hdi I

Hay tinh the tfch khdi chdp :

C. A'B'C theo V.

Cdu hdi 2

Hay tinh the tfch khdi chdp :

C. A'B'BA theo V

Cdu hdi 3

So sanh the tfch ciia hai khdi

C.ABFE va C.A'B'FE.

Hoat ddng ciia HS


\c. A'B'C ) ~ T ^


1 2 V/ x = V - - V - — V ^(C. A'B'BA ) ^ 3 3


Thd tfch hai khdi nay bing nhau..

48

Cdu hdi 4

Hay tfnh the tfch khdi chdp :

C. ABFE theo V.


X(CABFE) " " 3 ^

caub. Hoat ddng cua GV

Cdu hdi 1

Hay tfnh the tfch ciia (H)

Cdu hdi 2

Hay tfnh thd tfch khdi chdp :

C. C'E'F' theo V.

Cdu hdi 3

Tfnh ti sd hai the tich da cho.

Hoat ddng cua HS


V(„, = v-iv = fv


4 ^(C.CE'F) " ^-^(CCA'B') " T ^


V, 1

V2 2

HOATDQNG 4

TbM TflT Bfll HQC

1. a) Ndu (H) la khdi lap phucmg cd canh la 1 thi V/ jx = 1.

b) Nd'u (H) = (H) thi V(H) = V(H,)

c) Nd'u (H) dugc phan chia thanh hai khdi da dien (H,) va (Hj) thi

V(H)-V(H,)+V(H^)

Sd ducmg V^H) "oi ^r^" ^bc ggi la thd tfch cua khdi da didn (H).

Thd tich khdi lap phucmg cd canh la 1 ggi la khdi lap phuong don vi.

49

2. Thd tfch ciia khdi hdp chii nhat bing tfch ciia ba kfch thudc.

3. Thd tfch khdi lang tru cd didn tfch day B va chieu cao h la V = B.h.

4. The tfch khdi chdp cd didn tfch day la B, chidu cao h la

V=-B.h . 3

HOAT DONG 3

MQT SO CflU H 6 | TRflC NGHIEM

Hay dien dung (D), sai (S) vao cac khang dinh sau :

Cdu 1. Cho hinh ve ciia mdt hinh bat dien ddu cd the tfch la V A

(a) V,

(b) V,

V '(A.BCDE) ~ 2

_ v_ "(F.BCDE) ~ 2

V (C) ^ ( A . B C E ) = ' ^

V (d) V(A.ciD)=y

D

D

D

D

^

50

Trd ldi.

a

D

b

D

c

D

d

D

Cdu 2 Cho hinh ve cua mdt hinh bat dien ddu cd the tich la V

^^) Y(A.BCDE) ~ ^(F.BCDE)

(b) ^(A.CDE) "= '^(A.BCE)

^^' ^(A.CDE) ~ ^(F.BCE)

(") ^(F.CDE) ~ ^(A.BCE)

Trd ldi.

a

D

b

D

c

D

d

D

Cdu 3 . Cho hinh ve la hinh chdp tii giac ddu cd thd tich la V

D D D D

51

(a) ^(S ABC) "^(S.DBC)

(b) V(s DOA) = '^(S.BOC)

(C) %AOC) = V D B )

(d) '^(S.CDO) " '^(S.BCO)

Trd /oi

a

D

b

D

c

D

d

D

Chgn cdu trd ldi ddng trong cdc cdu sau:

Cdu 4. Cho hinh lang tru cd thd tfch la V

Q

D

D

n

Hinh sau cd thd tfch khdng phai la —

(a) A'. ABC

(c) B. A'B'C

Trdldi (d).

(b) C. ABC

(d) A'. BCCB'.

52

Cdu 5 . Cho hinh lang tru c6 th^ tfch la V.

PTuih sau c6 thd tfch Ik

(a) A'. ABC

(c) B. A'B'C

Trd ldi. (d).

Cdu 6 . Cho hinh vg :

2V

Hinh trdn c6 thd tfch Ik

(a) abc

(c) —abc 2

Trd ldi. (d).

(b) C. ABC

(d) A'. BCCB'.

(b)bca

(d) -abc 3

53

Cdu 7 Cho hinh ve vdi E, F la trung didm ciia cae canh SB va SC.

s

Khdi S.AEF cd the tich la

(a) abc

(c) — abc

(b) — bca 24

(d) —abc 12

Trd ldi. (b).

Cdu 8. Cho hinh ve vdi E, F la trung diem cua cac canh SB va SC. s

Khdi AEFCB cd the tich la

(a) abc

(c) — abc 8

Trd ldi (c).

(b) — bca 12

(d) —abc 12

54

Cdu 9. Cho hinh chdp S.ABCD nhu hinh ve. Day ABCD la hinh vudn , c^nh a

s

Canh SA bing : (a) a; (b) 2a;

(c) aV2 ; (d) a^B

Trd ldi. (d). Cdu 10. Cho hinh chdp S.ABCD nhu hinh ve. Day ABCD la hinh vudng canh a.

s

Thd tfch khdi chdp la

(a)a^ (b)ia^

(c) i^V2

(d) a'S

Trd ldi. (d).

55

Cdu 11 . Cho hinh chdp S.ABCD, day ABCD la hinh vudng canh a (hinh ve)

S

The tfch hinh chdp S.BCD la

(a)a^

(c)

(b)ia^ 6

'VI (d) 'V^

6 ' 6

Trd ldi. (d).

Cdu 12. Cho hinh hdp canh la 1, 2, 3 nhu hinh ve.

B; c

A'

Thd tfch khdi chdp D.AA'B' la

(a)0

(c)2

Trd ldi. (b).

(b)l

(d)3.

56

Cdu 13 Cho hinh hdp canh la 1, 2, 3 nhu hinh ve. B' C

The tfch khdi hop chit nhat la

(a) 3 (b) 4

(c) 5 (d) 6.

Trdldi (d).

Cdu 14. Cho hinh hdp canh la 1, 2, 3 nhu hinh ve.

B" C

A'. ^^^^ ^^

^^^ 1 \ ^^^^

7\'3 \ ' ^ < v ^

' l \ •• / 1 ^ ^ >

/ 1 ^ v ^ ^

I 1 . > 5 - - ^ - ' 2 . ! y B x \

D'

- ^

ti sd thd tfch ciia khdi chdp D.AA'B' va phin cdn lai la

1 <

(c) 1

(b)

y. Trd ldi. (b).

57

HOATDCDNG 3

naOFNG DflN GIfll Bfll T6P SflCH GIflO KHOfl

Bai 1. Sii dung true tie'p cdng thiic tfnh the tfch khdi chdp. s

Gia sii ta cd tti dien ddu S.ABC canh a.

Hoat ddng cua GV

Cdu hdi 1

Hay tfnh canh AI.

Cdu hdi 2

Hay tfnh dien tich day.

Cdu hdi 3

Tfnh dudng cao SH.

Cdu hdi 4

Tfnh thd tfch hinh chdp.

Hoat ddng cua HS


2


4


f—

SH = VSA2 A H 2 = " ^ V

3


a3V2

12

58

Bai 2. Su dung true tie'p cdng thiic tinh thd tfch khdi chdp.

A

Gia sit ta cd bat dien ddu canh a nhu hinh ve.

Hoat ddng cua GV

Cdu hdi I

Chia bat dien ddu thanh hai khdi chdp tii giac ddu canh a. Chiing minh the tfch hai khdi chdp bing nhau.

Cdu hdi 2

Hay tfnh dien tich day.

Cdu hdi 3

Tfnh dudng cao AI.

Cdu hdi 4

Tfnh thd tfch hinh chdp.

Hoat ddng cua HS


HS tu chiing minh..


S = a 2


aV2 Al = ^ ^

2


a^V2 V= Tuf dd suy ra thd tfch khdi

6

bat dien ddu.

59

Bai 3. Sit dung true tie'p cdng thiic tfnh thd tfch khdi chdp va thd tfch hinh hgp.

B' C

Gia sit ta cd hinh ve.

Hoat ddng ciia GV

Cdu hdi I

Chiing minh cac thd tfch eac tii didn : AA'B'D' CC'B'D' D'ADC, B'ABC bing nhau.

Cdu hdi 2

Gia sit thd tfch hinh hop la V thi the tfch mdi hinh tren la bao nhieu?

Cdu hdi 3

Thd tfch hinh chdp ACB'D' la bao nhieu?

Cdu hdi 4

Tfnh tl sd hai thd tfch

Hoat ddng ciia HS

Ggi y trd lai cdu hdi I

HS tu chiing minh.

Goi y trd ldi cdu hdi 2

iv 6 Ggi y trd ldi cdu hoi 3

1 V V -v.= — 3 3


Ti sd 3.

60

Bai 4. Hudng ddn. Sit dung true tidp cdng thiic tfnh thd tfch hinh chdp

A

Gia s\l ta cd hinh ve.

Hoat ddng ciia GV

Cdu hdi I

Chiingminh^^SB'C=SB'.SC'

ASBC SB.SC

Cdu hdi 2

Chiing minh — =

h SA

Cdu hdi 3

Chiing minh bai toan trdn.

Hoat ddng cua HS


HS tu chiing minh bing each ve them dudng cao ciia mdi tam giac tii C va C


HS tu chiing minh.


HS tu chiing minh.

Bai 5. Hudng ddn. Six diing true tidp cdng thiic tfnh thd tfch hinh chdp

D

Gia sii ta cd hinh ve.

61

Hoat ddng cua GV

Cdu hdi I

Chirng minh CE 1 mp(ABD).

Cdu hdi 2

DA

Cdu hdi 3

T'v, DF Tmh DB

Cdu hdi 4

rr- u . ' - u - .u^ ' . ' u V E F C ) Tinh tl so hai the tich

^(DBAC)

Cdu hdi 5

Tinh thd tfch tii dien CDEF.

Hoat ddng cua HS


^ , JBAIAC ^^ , _ Ta CO - => BA -L CE

[BA 1 DC

Lai cd CE ± AD nen A D l mp(DAB).


CD^

DE DA _ a^ _ 1 DA DA 2a^ 2


DF CD^ a^ 1

DB DB^ 3a2 3


' (DEFC) DF.DE.DC _ 1

V(DBAC) DB.DA.DC 4


1 1 3 V E F ) = 4 ^ ^ ^ ^

Bî 6. Hudng ddn. Six dung true tie'p cdng thiic tfnh thd tfch hinh chdp

Gii sft ta cd hkih ve.

62

Hoat ddng cua GV

Cdu hdi I

Chiing minh thd tfch hai khdi chdp DABC va DCBE bing nhau.

Cdu hdi 2

Chiing minh thd tfch khdi chdp

DCBE khdng ddi.

Hoat ddng cua HS


HS tu chiing minh.


Tam giac ECD cd EC = a, CD = b.

ECD = (d,d') khdng ddi do dd dien

tfch tam giac ECD khdng ddi.

Dudng cao ha tit B de'n day (ECD) la khoang each giiia d va mp(ECD) khdng ddi.

Tii dd ta dugc dpcm.

63

On tap chrfcrng I (tiet 9,10)

I. MUG Tl£u

1. Kien thurc

HS nam dugc:

Khai niem :

+. Hinh da dien va khdi da dien trong khdng gian.

+ Hai khdi da didn bing nhau.

+ Phan chia mdt khdi da dien thanh nhidu khdi da didn khac nhau.

+ Khdi da dien Idi

+ Khdi da dien ddu.

+ Thd tfch cac khdi da didn : Thd tfch hinh hdp, hinh chdp va hinh lang tni.

Mdt sd dinh If va mdnh dd quan trgng:

+ Qua phep ddi hinh thi ta dugc hai khdi da didn bing nhau.

+ Hai khdi da didn bing nhau thi cd thd tfch bing nhau.

+ Chi cd 5 loai khdi da didn ddu.

+ Thd tfch hinh hop, hinh chdp va hinh lang tru.

2. KT nang

• Tfnh thanh thao the tfch mdt sd khdi da didn : Hinh hdp chii nhat, khdi chdp va khdi lang tru.

• Mdl quan he giiia the tfch cua cac khdi dd.

• Mdl quan hd gifla the tfch va didn tfch.

• Mdi quan hd giua thd tfch va khoang each.

64

3. Thai do

• Lidn he dugc vdi nhidu vah dd cd trong thuc te vdi mdn hgc hinh hgc khdng gian.


• Hiing thii trong hgc tap, tfch cue phat huy tfnh dgc lap trong hgc tap.

n. CHUXN BI CUA GV VA n&

1. Chuan bi ciia GV:

• Chuin bi dn tap toan bd kien thiic trong chucmg.

• Chudn bi mdt den hai bai kidm tra.

• Cho hgc sinh kiem tra va chain, tra bai.

2. Chuan bi ciia HS :

On tap lai toan bd kie'n thiic trong chuong, giai va tra ldi cac cau hdi bai tap trong chuang.

in. PHAN PHOI TH6I LUONG

Bai nay chia thanh 2 tie't:

Tiet 1 : On tap.

Tiet 2 : Kidm tra 1 tiet.

IV. TifN TDlNH DAY HOG

n. DMT VPTN D €

cau hdi 1.

Em hay nhic lai: Cac khai nidm khdi da dien, khdi chdp, khdi lang tru va khdi hop chii nhat.

cau hoi 2.

Ndu mdl quan he giita thd tfch khdi lang tru va khdi chdp cd cung day.

cau hdi 3.

Hay nhic lai cac khai- nidm khoang each. Tit dd em cd them phucmg phap nao tfnh khoang each dua vao thd tfch.

65

HOAT CHDNG 1

1. On tap kien thiirc ccJ ban trong chi/dng

a) Tdm tat li thuye't co ban.

1. a) Hai da giac phan biet chi cd the : Hoac khdng cd didm chung hoac cd mdt

canh chung.

b) Mdi canh ciia da giac nao cung la canh chung cua diing hai da giac.

2. ITinh da dien la hinh dugc tao bdi cac da giac thda man 2 tfnh chit tren.

Khdi da dien la phan khdng gian dugc gidi ban bdi hinh da dien, kd ca hinh da

dien do.

3. Trong khdng gian, quy tic dat tuong ung mdi didm M vdi duy nhat mdt didm

M' dugc ggi la phep bien hinh trong khdng gian.

Phep bien hinh trong khdng gian la phep ddi hinh ne'u nd bao toan khoang each.

4. Phep tinh tien theo vecto v la phep bien hinh bie'n M thanh M' ma MM' = v

5. Phep ddi xiing tam O la phep bien hinh bien O thanh chfnh nd. Bie'n mdi didm

M khac O thanh M' ma O la trung diem ciia MM'

6. Phep ddi xiing qua dudng thing A la phep bie'n hinh bie'n mdi didm thudc A

thanh chinh nd. Bien mdi didm M khdng thudc A thanh didm M' ma A la dudng

trung tryc cda MM'

7. Thuc hien lien tiep cac phep ddi hinh ta dugc phep ddi hinh.

Phep ddi hinh bien da dien (H) thanh da dien (H') va dinh, canh, mat ciia (H)

thanh dinh, canh, mat ciia (H').

8. Hai hinh dugc ggi la bing nhau neu nd cd mdt phep ddi hinh bie'n hinh nay

thanh hinh kia.

66

9. Khdi da didn (H) dugc ggi la khdi da dien ldi ne'u mdt doan thing ndi hai didm ba't ki thudc (H) ddu nim trgn trong (H).

10. Khdi da didn ddu la khdi da didn ldi cd tfnh chat sau:

a) Mdi mat ciia nd la mdt da giac ddu p canh.

b) Mdi dinh ciia nd la dinh chung cua diing q mat.

Khdi da didn ddu nhu vay ngudi ta ggi la khdi da dien ddu loai {p, q}.

11. Chi cd nam loai da didn ddu {3,3}, {4,3}, {3,4}, {5,3} va {3,5}.

12. a) Nd'u (H) la khdi lap phuong cd canh la 1 thi Ny^^ = 1.

b)Nd'u(H) = (H') thi V(H) = V(H,)

c) Neu (H) dugc phan chia thanh hai khdi da dien (H,) va (H2) thi

V(H)=V(H,)+V(H^)

Sd duong V/^\ ndi trdn dugc ggi la thd tfch cua khdi da dien (H).

Thd tfch khdi lap phuong cd canh la 1 ggi la khdi lap phuong don vi.

13. Thd tfch cua khdi hdp chii nhat bing tfch cua ba kfch thudc.

14. Thd tfch khdi lang tru cd didn tfch day B va chidu cao h la V = B.h.

15. Thd tfch khdi chdp cd didn tfch day la B, chidu cao h la

V - - B . h . 3

b) cau hdi tr^c nghiem nh^m dn tap kie'n thurc:

GV ndn dua ra mdt he thdng cau hdi trie nghiem nhim dn tap toan bd kie'n thiic trong chuong.

Sau day xin gidi thidu mgt sd cau hdi:

67

L HAY KHOANH TRON CAU DUNG, SAI TRONG CAC CAU SAU MA

EM CHO LA HOP LL

Cdu 1. Mgi phep bien hinh deu dugc hai khdi da dien bang nhau.

(a) Diing (b) Sai.

Cdu 2. Phep tinh tien theo vecto v ddu dugc hai khdi da dien bing nhau.

(a) Diing (b) Sai.

Cdu 3. Phep ddi xiing tam O dugc hai khdi da dien bing nhau.

(a) Diing (b) Sai.

Cdu 4. Phep ddi xiing qua dudng thing dugc hai khdi da dien bing nhau.

(a) Diing (b) Sai.

Cdu 5. Phep ddi xiing qua mat phang dugc hai khdi da dien bing nhau.

(a) Diing (b) Sai.

Cdu 6. Qua hai phep bien hinh : Phep tinh tie'n theo vecto v va phep ddi xiing tam O dugc hai khdi da dien bing nhau.

(a) Diing (b) Sai.

Cdu 7. Qua hai phep bien hinh : Phep tinh tie'n theo vecto v va phep ddi xung qua dudng thing dugc hai khdi da dien bing nhau.

(a) Diing (b) Sai.

Cdu 8. Qua hai phep bie'n hinh : Phep ddi xiing tam O va phep ddi xiing qua dudng thing dugc hai khdi da dien bing nhau.

(a) Diing (b) Sai.

Cdu 9. Khdi da dien ludn chiia trgn mgi doan thing cd hai diu thudc khdi da dien la khdi da dien ldi.

(a) Diing (b) Sai.

Cdu 10. Khdi da dien ludn chiia trgn mgi dudng thing la khdi da dien Idi.

(a) Diing (b) Sai.

Cdu 11. Khdi tii dien cd 4 mat la tam giac ddu la khdi da dien ddu

(a) Dung (b) Sai.

Cdu 12. Co vd sd khdi da dien ddu

(a) Diing (b) Sai.

68

Cdu 13. Chi cd 5 khdi da dien ddu

(a) Dung (b) Sai.

Cdu 14. Khdi da dien ddu cd sd dinh va sd mat bing nhau

(a) Dung (b) Sai.

Cdu 15. Da dien cd cac mat la tam giac thi tdng sd cac mat phai la sd chan.

(a) Dung (b) Sai.

Cdu 16. Da dien cd mdi dinh la dinh chung cua sd mat le thi tdng sd cac dinh

phai la sd chan.

(a) Diing (b) Sai.

Cdu 77.'Trung didm cac canh ciia mdt tii dien ddu la dinh ciia mdt tii dien deu.

(a) Diing (b) Sai.

Cdu 18. Hinh lap phuong la mdt da dien ddu.

(a) Diing (b) Sai.

Cdu 19. Hinh lap phuong la luc dien ddu.

(a) Dung (b) Sai.

Cdu 20. Hinh lap phuong la da dien ddu dang {12, 8}

(a) Diing (b) Sai.

Cdu 21. Hinh lap phuong la da didn ddu dang {4, 3}

(a) Dung (b) Sai.

Cdu 22. Hinh lap phuong la da dien ddu dang {3,4}

(a) Diing (b) Sai.

Cdu 23. Hinh bat dien ddu la da dien ddu dang {4,3}

( a) Diing (b) Sai.

Cdu 24. Hinh bat dien ddu la da dien ddu dang {4,3}

(a) Diing (b) Sai.

Cdu 25. Hinh 12 mat ddu la da dien ddu dang {5,3}

(a) Diing (b) Sai.

69

Cdu 26. Hinh 12 mat ddu la da dien ddu dang {3, 5}

(a) Diing (b) Sai.


(a) Diing (b) Sai.


(a) Diing (b) Sai.

Cdu 29. Hinh hop chu nhat kfch thudc 2, 3, 4 cd thd tfch la 24

(a) Dung (b) Sai.

Cdu 30. Hinh hop chit nhat kfch thudc 2, 3, 4 cd thd tfch la 12

(a) Diing (b) Sai.

Cdu 31. Hinh lang tru la hinh hop.

(a) Dung (b) Sai.

Cdu 32. Hinh lap phuong la hinh lang tru

(a) Diing (b) Sai.

Cdu 33. Trong hinh lang tru dimg, cac mat ben vudng gdc vdi day.

(a) Diing (b) Sai.

Cdu 34. Trong hinh lang tru diing, cac canh ben song song vdi nhau.

(a) Diing (b) Sai.

Cdu 35. Trong hinh lang tru diing, cac each ben vudng gdc vdi day.

(a) Diing (b) Sai.

Cdu 36. Hinh hop chii nhat cd cac mat ben la hinh chii nhat.

(a) Dung (b) Sai.

Cdu 37. Hinh lap phuong cd cac mat la hinh vudng.

(a) Diing (b) Sai.

Cdu 38. Hinh chdp ddu cd cac mat ben la tam giac ddu.

(a) Diing (b) Sai.

Cdu 39. Hinh chdp ddu cd cac mat ben la tam giac can.

(a) Dung (b) Sai.

70

Cdu 40. Hinh chdp tii giac ddu la hinh chdp ddu

(a) Dung (b) Sai.

Cdu 41. Hinh chdp tii giac ddu canh a cd thd tich la - a

(a) Diing (b) Sai.

Cdu 42. Mdt hinh chdp cd chung day vdi hinh lang tru. Dinh cua hinh chdp thugc

day cdn lai cua hinh lang tru. The tfch khdi lang tru va khdi chdp bing nhau (a) Dung (b) Sai.

Cdu 43. Mdt hinh chdp cd chung day vdi hinh lang tru. Dinh cua hinh chdp thudc

day cdn lai ciia hinh lang tru. Thd tich khdi lang tru gap 3 lan khdi chdp.

(a) Dung (b) Sai.

Cdu 44. Mdt hinh chdp cd chung day vdi hinh lang tru. Dinh ciia hinh chdp thugc

day cdn lai ciia hinh lang tru. The tich khdi lang tru gap 6 lan khdi chdp.

(a) Diing (b) Sai.

Cdu 45. Hinh lang tru cd dien tich day la 6, the tich la 24. Khoang each tir mdt

didm ciia day nay de'n day kia la 4

(a) Diing (b) Sai.

Cdu 46. Hinh lang tru cd dien tich day la 6, the tich la 24. Khoang each tir mdt

didm cua day nay de'n day kia la 6

(a) Diing (b) Sai.

Cdu 47. Hinh lang tru cd dien tfch day la 6, the tfch la 24. Khoang each tir mgt

didm cua day nay de'n day kia la 12

(a) Dung (b) Sai.

Cdu 48. Hinh chdp cd dien tfch day la 6, the tfch la 24. Khoang each tir dinh de'n

day la 6

(a) Diing (b) Sai.

Cdu 49. Hinh chdp cd dien tfch day la 6, thd tfch la 24. Khoang each tir dinh den

day la 12

(a) Dung (b) Sai.

71

Cdu 50. Hinh chdp cd dien tfch day la 6, thd tfch la 24. Khoang each tii dinh de'n

day la 18

(a) Diing (b) Sai.

Cdu 51. Cho OA, OB va OC ddi mdt vudng gdc vdi nhau, H la true tam tam giac

ABC. Khi dd HO 1 (ABC).

(a) Diing (b) Sai.

Cdu 52. Mdt tii dien ed ba canh ddi mdt vudng gdc vdi nhau ggi la tii didn vudng.

Tii dien vudng la tii dien ddu.

(a) Dung (b) Sai.

Cdu 53. Tii dien vudng la hinh chdp ddu.

(a) Diing (b) Sai.

Cdu 54. Tix dien vudng cd ba mat la cac tam giac vudng.

(a) Diing (b) Sai.

Cdu 55. Tii dien ddu cd cac mat la eac tam giac ddu.

(a) Dung (b) Sai.

Cdu 56. Hinh chdp tam giac ddu cd cac mat la cac tam giac ddu.

(a) Diing (b) Sai.

Cdu 57. Hinh chdp tam giac ddu cd cac mat la cac tam giac can.

(a) Diing (b) Sai.

Cdu 58. Hinh chdp tii giac ddu cd day la hinh vudng.

(a) Diing (b) Sai.

Cdu 59. Hinh chdp tii giac ddu cd dudng cao la dudng ndi dinh va tam ciia day.

(a) Dung (b) Sai.

Cdu 60. Hinh chdp tam giac ddu ed day la tam giac ddu.

(a) Diing (b) Sai.

Cdu 61. Hinh chdp tam giac ddu cd dudng ndi dinh va tam vudng gdc vdi day.

(a) Diing (b) Sai.

72

Cdu 62. Cho hinh chdp SABCD, day ABCD la hinh vudng tam O. SA 1 (ABCD).

SABCD la hinh chdp ddu.

(a) Diing (b) Sai.

Cdu 63. Cho hinh chdp SABCD, day ABCD la hinh vudng tam O. SO 1 (ABCD). SABCD la hmh chdp ddu.

(a) Diing (b) Sai.

Cdu 64. Cho hinh chdp SABCD, day ABCD la hinh vudng tam O. SA 1 (ABCD). SABCD khdng la hinh chdp ddu.

(a) Diing " (b) Sai.

H. D I £ N DUNG, SAI VAO 6 THICH HOP

Hdy dien dting, sai vdo cdc d trdng sau ddy md em cho Id hgp li nhdt.

Cdu 65. Cho hinh chdp S.ABCD, day ABCD la hinh vudng canh a, SA = a

SA l(ABCD).

(a) Thd tfch hinh chdp la a

(b) Thd tfch hinh chdp la - a' 3

(c) Thd tfch hinh chdp la — a 6

(d) Ca ba cau trdn ddu sai.

Trd ldi.

• D

D D

a

S

b

S

c

D

d

S

73

Cdu 66. Cho hinh hop chit nhat ABCDA'B'CD' cd AA' = c, AB = a, AD - b B' a

y^\ D

y' B

' y^

(a) Thd tfch hinh hop la abc

(b) The tfch hinh chdp A'.ABCD la abc

(c) Thd tfch hinh chdp A'.ABCD la - abc

(^) ^(ABCD.A'B'CD) ^ ^ ^ ( A ' . A B C D )

Trd ldi.

a

D

b

S

c

D

d

D

D D

D

D

Cdu 67. Cho hmh hop chit nhat ABCDA'B'CD'. B'

A'

- ' B

C

(a) Thd tfch hinh hdp la abc

(b) The tfch hinh chdp A'.ABD la abc •

74

(c) Thd tfch hinh chdp A'.ABD la - abc 6

(^)^(ABCD.A'B'C'D) =6^(A'.ABD)

Trd ldi.

a

a

D

b

S

c

D

d

D

Cdu 68. Cho hinh chdp S.ABCD, day ABCD la hinh vudng canh a, SA = a vudng gdc vdi day.

S

(a) SB = aV2

(b) SD = aV2

(c) Didn tfch tam giac SBD bang


a^Vi

n D

D

D

Trdldi.

a

D

b

D

c

D

d

S

75

Cdu 69. Cho hinh chdp S.ABCD, day ABCD la hinh vudng eanh a, SA = a vudng gdc vdi day.

s

(a) SB = aV2

(b) SD = aV2

(c) Didn tfch tam giac SBD bing a^V3

D D

n

(d) Thd tfch hinh chdp S.ABD bing

Trd ldi.

a

D

b

D

c

D

d

D

•

Cdu 70. Cho hinh chdp S.ABCD, day ABCD la hinh vudng canh a, SA = a vudng gdc vdi day.

S

76

(a) Dien tfch tam giac SBD bang a^Vs

(b) The tfch hinh chdp S.ABD bing — 6

(c) Khoang each tuf A ddn mp(SBD) la

(d) Ca ba eau trdn ddu sai.

Trd ldi.

2^

D

• D

n

a

D

b

D

c

D

d

S

Cdu 69. Cho hinh chdp SABCD, day ABCD la hinh vudng tam O, SA 1 (ABCD). S

((a) Tam giac SCD la tam giac vudng

(b) Tam giac SCB la tam giac vudng

(c) ASCD = ASBC


Trd ldi.

• • D D

a

D

b

D

c

D

d

S

Cdu 71. Cho hinh lap phuong ABCDA'B'CD' canh a. B'

A A' 1

)._ _ _ / 'B

/ /

/ /

/

D'

(a) Thd tich khdi lap phuong la a'

1 3 (b) Thd tfch khdi chdp A'.ABCD la - a 3

1 (c) Thd tfch khdi lang tru ABDA'B'D' la -a^

6

(d) Ca ba cau trdn ddu sai

Trd ldi. a

D

b

D

c

D

d

S

Cdu 72. Cho hmh lap phuang ABCDA'B'CD' canh a.

B'

A A ;

/ B /

/ / /

C

/

D'

D

D

D

D

78

(a) Thd tfch khdi lap phuong la a

1 3 (b) The tfch khdi chdp A'.DD'C la - a

6

(c) Thd tfch khdi lang tm AA'B'.DD'C la -a^ 6

(d) Ca ba cau trdn ddu sai

Trd ldi.

a

D

b

D

c

D

d

S

0

D

n 0

///. CAU HOI DA WA CHON


Cdu 73. Cho hinh chdp SABCD, day ABCD la hinh thang vudng tai A,

SA l(ABCD), SA = a, AB = 2a, AD = DC = a. Khoang each tit C den (SAD) la

(a) a;

(c) a ^ ;

Trdldi (a).

Cdu 74. Cho hmh chdp SABCD, day ABCD la hinh thang vudng tai A,

SA l(ABCD), SA - a, AB = 2a, AD = DC = a. Khoang each tii B ddn (SAD) la

79

D C

(a) a ; ^ (b) 2a

(c) aV3 ; (d)aV2.

Trd ldi (b).


SA l(ABCD), SA = a, AB = 2a, AD = DC = a. Khoang each tit A ddn (SBC) la s

(a) a;

(c) aV3 ;

Trd ldi. (d).


SA l(ABCD), SA = a, AB = 2a, AD = DC = a. Khoang each tit B ddn (SAC) la

80

(a) a;

(c) aV2 ;

Trd ldi. (c).


SA l(ABCD), SA = a, AB = 2a, AD = DC = a. Thd tfch khdi chdp la

(a)y (b)

( c ) - ; (d) Ca ba cau trdn ddu sai.

Trd ldi. (a).


SA J.(ABCD), SA = a, AB = 2a, AD = DC = a. Thd tfch khdi chdp S.ADC la

81

(a) (b)

(c) (d) Ca ba cau tren ddu sai.

Trd ldi. (c).


SA l(ABCD), SA = a, AB = 2a, AD = DC = a. Thd tfch khdi chdp S.ABC la

S

c4 (b)

(c) (d) Ca ba cau tren ddu sai.

Trd ldi (b).


SA l(ABCD), SA = a, AB == 2a, AD = DC = a. Khoang each giua SA va BC la

82

(a) a;

(c) aV2 ;

Trdldi (d).


SA l(ABCD), SA = a, AB = 2a, AD = DC = a. Didn tich tam giac SBC la

(a) a^;

(c) a^yfl ;

(b) 2a'

(d) 1^76

Trd ldi. (d).


SA l(ABCD), SA = a, AB = 2a, AD = DC = a. Khoang each ttr A de'n mat phing (SBC) la

83

(a) a';

(c) 3^72 ;

Trd ldi (d).

aV2

(b) 2a'

(d) 1^76

Trd ldi (d).

Cdu 83. Cho hinh chdp SABCD, day ABCD la hinh vudng canh a, SA l(ABCD),

SA = a. Khoang each giiia AB va SD la

s

(a) a;

(c) aV2 ;

Trd ldi (d).

84


SA = a. Khoang each giiia BC va SD la S

(a) a;

(c) aV2 ;

Trd ldi (a).

Cdu 85. Cho hinh chdp SABCD, day ABCD la hinh vudng tam O canh a,

SA l(ABCD), SA = a. Khi dd SO bing

(a) a;

(c) ayfl ;

Trdldi (d).

85

HOATDQNG 2

2. Hirdng dan tra ldi cau hoi va bai tap on tap chUdng 1

Bai 1. Hudng ddn.

+ Xem lai cac khai niem da dien la gi?

+ Khai niem mat va dinh ciia da dien.

Bai 2. Hudng ddn.

+ Xem lai cac khai niem da dien la gi?

+ Khai niem mat va dinh cua da dien.

Vf du : Hinh tao bdi hai binh chii nhat

Bai 3. Hudng ddn.

+ Xem lai cac khai niem vd khdi da didn Idi.

GV tu cho HS neu vi du.

Bai 4. Hudng ddn.

+ Xem lai cac khai niem thd tfch khdi chdp va khdi lang tru.

+ Mdl quan he giiia chiing.

Bai 5. Hudng ddn.

+ Xem lai cac khai niem : Hinh chie'u vudng gdc ciia dudng thing tren mat phang.

+ Dinh If vd thd tich hinh chdp.

86

Hoat ddng ciia GV Hoat ddng ciia HS

Cdu hdi 1

Tinh thd tich khdi chdp OABC.

Cdu hoi 2

Tfnh OE'

Cdu hdi 3

Tinh AE.

Cdu hdi 4

Tfnh didn tich tam giac ABC.


^(OABC) = g ^ b c


^ . 1 1 1 Taco j = ^ + -^

OE^ b^ c^ 2 7

Txx 66 ta cd OE^ = ^ ^ b +c


.2„2

Tacd A E ^ = O E 2 + a 2 = ^ - + a^ b^+c^

Tit doa ta cd :

AE = a V + b V + c V

b^+c^


S = -AE.BC 2

' . 2 . 2 , u2„2 , „2„2 1 l a ^ b ^ ^ b V ^ c X / b ^ ^ c ^

b^+c^

87

Cdu hdi 5

Tinh OH

4^ a V + b V + c V


3V abc 0 H =

V^2^^^c2+cV

Bai 6. Hudng ddn.

+ Xem lai cac khai niem : Hinh chdp tam giac ddu

+ Dinh If vd thd tfch hinh chdp.

+ van dung Bai tap 4 muc 3 SGK.

s

cau a.

Hoat ddng cua GV

Cdu hdi 1

van dung bai toan 4 trong SGK hay vie't ti sd hai thd tfch.

Cdu hdi 2

TfnhAE.

Cdu hdi 3

Tfnh AH.

Hoat ddng ciia HS


(SDBC) _ SD.SB.SC _ SD

V(sABC) SA.SB.SC SA


2


AU 2 . „ aV3 A H - - A E - ^ .

3 3

88

Cdu hdi 4

Tfnh SA, tuf dd suy ra do dai cua cac canh bdn.

Cdu hdi 5

Tfnh SD.

Cdu hdi 6

Tfnh ti sd hai the tfch.


SA = AH : cosdO" = ^ ^ 3

Cac canh ben cd do dai bing nhau va

^. 2aV3 bang — ^


Ta cd

AD = AB.cosSAB

a aV3 -a.- 2a V3

Tit dd ta cd

SD = SA-AD:

_ 5 a ^ 12

2aV3 aV3


SA _ 2aV3 12 ^ 5 S D " 3 "5373" 8

Ta cd

caub.

Hoat ddng ciia GV

Cdu hdi 1

TfnhSH.

Cdu hdi 2

Tfnh thd tfch hinh chdp S.ABC.

Hoat ddng cua HS


SH = AH.tandO" = — 4


12

89

Cdu hdi 3

Tfnh thd tfch hinh chdp S.SBC.


V' = V3 96

Bai 7. Hudng ddn. Six dung tfnh chit hinh chieu trong khdng gian. Cdng thiic tfnh

thd tfch. S

Ke SH ± mp(ABC), HE 1 AB, HF 1 BC va HJ 1 AC.

Hoat ddng cua GV

Cdu hdi I

Em cd nhan xet gi vd SE, SF va

SJ. Cdu hdi 2

Tfnh chu vi tam giac ABC.

Cdu hdi 3

Tfnh HE.

Hoat ddng cua HS


Vi cac gdc SEH,SFH, SJH bing nhau

nen : SE = SF = SJ.

Goi y trd ldi cdu hdi 2

Chu vi tam giac ABC la : 18a; nita chu vi la 9a.

Ggi y trd loi cdu hdi 3

AABC ^ P-HE .

Ta cd p = 9a, S^^gc - 6V6a

rr v « . . . ITT: ÂABC 2a\/6a Tu do ta CO : HE = = P 3

90

Cdu hdi 4

Tfnh SH.

Cdu hdi 5

TfnhV


Ta cd SH = HE tandO" = 2V2a .


V = 8V3a^

Bai 8. Hudng ddn. Six dung tfnh cha't hinh chie'u trong khdng gian. Cdng thiic tfnh thd tfch.

s

Ke SH 1 mp(ABC), HE 1 AB, HF 1 BC va HJ 1 AC.

Hoat ddng ciia GV

Cdu hdi I

Cdu hdi 2

Tfnh SB va SB'

Hoat ddng cua HS


V = - a b c . 6


Ta cd SA^ = SB'.SB hay SB' = SB

Tacd SB = Va^+c^ Tit dd tacd :

c2 S B ' -

Va2+c2

91

Cdu hdi 3

Tinh SD va SD'

Cdu hdi 4

Tfnh SC va SC

Cdu hdi 5

Tfnh thd tfch khdi chdp

SAB'C'D'


Tuong tu ta cd : 9

SB = Vb2+c2 SB' = - ^ = ^ = = Vc + D


SC ± A C

SC = Va^+b^+c^ ; c2

SC -Va2+b2+c2


Tacd

%AB'CD) SA.SB'.SC'.SD'

V SA.SB.SC.SD

Tii dd ta tfnh dugc thd tfch khdi chdp

SAB'C'D'

Bai 9. Hudng ddn. Six dung tfnh chat hinh chie'u trong khdng gian. Cdng thiic tinh

the tfch.

Xem hinh ve

92

Hoat ddng ciia GV

Cdu hdi I

Chung minh SM Imp(AEMF)

Cdu hdi 2

Tfnh SB va SB'

Cdu hdi 3

TfnhEF.

Cdu hdi 4

Tfnh SC va SC

Cdu hdi 5

Tfnh AM.

Cdu hdi 6

TinhV(sAEMF)'

Hoat ddng ciia HS


Ta cd tam giac SAC la tam giac ddu

canh aV2 , do dd AM 1 SC.

Ta lai cd BD 1 mp(SAC) nen BD ±

SC ma BD // EF. Vay SC 1 EF. Hay

SC 1 mp(AEMF).


Ta cd SO va AM la cac dudng trung tuye'n cia ASAC, do dd ta cd :

EF SI 2 . „^ 2 a ^ —— = — = — hay EF = .

BD SO 3 3


Tuong tu ta cd : SB = Vb^T? SB' =


SC ± AC

4J^\

sc=V?4v7? SC' =

Va2+b2+c2


aVe AM= .

2 Ggi y trd ldi cdu hdi 6

V A E M F ) = ^ S M . A M . E F = ^

93

Bai 10. Hudng ddn. Six dung tfnh chat hinh chieu trong khdng gian. Cdng thiic tfnh thd tfch.

B

Xem hinh ve

cau a.

Hoat ddng cua GV

Cdu hdi I

Chiing minh

^(ABB'C) ^^ (C .A 'B 'C)

Cdu hdi 2

Hoat ddng ciia HS


HS tu chiing minh.


^(ABB'C) =^(C.A'B'C') ^ 2 ^(ABCA'B'C)

a'S 12


Cdu hdi 1

Tinh thd tfch khdi CAA'B'B.

chdp

Hoat ddng cua HS


2 V A A ' B ' B ) = V - V A ' B ' C ) = - V

94

Cdu hdi 2

T' u .' -' ^(C.A'B'FE) 1 inh tl so : — .

^(C.A'B'A)

Cdu hdi 3

Tfnh V(c.^,B.FE)theoV

Cdu hdi 4

Tinh V(c.A'B'FE)


' (C.A'B'FE) _ CE.CF 4

V(c.ABA) CA.CB 9


V - 4 2 ^ _ 8 V ^(C.A'B'FE) - 9 3 27 '

Gai y trd ldi cdu hdi 4

V _ 8 a3V3 V A ' B ' F E ) - 2 7 ' 4

Bai 11. Hudng ddn. Six dung tfnh chat hinh chieu trong khdng gian. Cdng thiic tfnh

thd tfch.

D C

Ggi O la tam hinh hop. Hinh ve.

caua.

Hoat ddng ciia GV

Cdu hdi 1

Chiing minh

Qua phep ddi xiing tam 0 , hinh

A'ECFA bie'n thanh hinh C.FA'EC

Cdu hdi 2

TInh ti sd hai thd tfch.

Hoat ddng cua HS


HS tu chiing minh.


Ti sd bing 1.

95

Bai 12. Hudng ddn. Six dung tfnh chat hinh chidu trong khdng gian. Cdng thiic tfnh

thd tfch.

B

Hinh ve.

cau a.

Hoat ddng cua GV

Cdu hdi I

Tfnh khoang each tit M ddn mp(ADN).

Cdu hdi 2

Tfnh didn tfch tam giac ADN.

Cdu hdi 3

Tuih V(j^^p^) .

Hoat ddng ciia HS


Khoang each dd la a.


sy. 2


V ^(M.ADN) ~ g


Cdu hdi 1

Chiing minh ME // DN.

Hoat ddng cua HS


Ta cd ME // DN do mp(ABCD) // mp(A'B'C'D')

96

Cdu hdi 2

Chiing minh FN // ED.

Cdu hdi 3

Chung minh A 'E = - ; B F = — 4 3

Cdu hdi 4

Tfnh V (F.DBN)

Cdu hdi 5

Tfnh V (D.ABFMA')

Cdu hdi 6

Tfnh V (D.A'ME)

Cdu hdi 7

Tfnh V(H)

Cdu hdi 8

Tfnh ti so hai thd tfch.


HS tu chiing minh.


Ta cd AFBN ~ ADD'E ;

AA'ME-ACDN. Tit dd ta cd

A'E CN BN ED' TTT7 ~ T; ;^ ' T:;7 = ^::— > ta cd dpcm. A 'M CD BF DD' Ggi y trd ldi cdu hdi 4

V ^(F.DBN) - J3


a2 Ta cd S^pMg. = — nen

'ABFMA' lla^

12 .Dodd

V lla^

(D.ABFMA') ~ og


„2

Ta cd S AA'ME 16 Dodd


V - ^5a'

V)-ii^ Ggi y trd ldi cdu hdi 8

Tl sd hai the tfch la : — 89

97

HOAT DONG 3

Tra ldi cau hoi trac nghiem chirdng I

1

B

2

A

3

A

4

C

5

B

6

C

7

C

8

D

9

B

10

B

HOATDQNG 4

Gidi thieu mot so de kiem tra chifcfng t

De sd 1

PhAN 1. Cau hdi va bai tap trac nghiem, mdi cau 1 diem.

Hay chon cau tra ldi dung trong cac cau sau:

Cdu I. Cho hinh lap phuang ABCDA'B'CD' canh a. Khi dd :

(a) Thd tich khdi lap phuong la a ;

(b) The tich khdi lap phuang la a ' ;

(c) The tich khdi lap phuong la a

(d) Ca ba cau tren ddu sai

,Cdu 2. Cho hinh chop SABCD, day ABCD la hinh vudng canh a, SA= 3a va vudng gdc vdi day.

(a) Thd tich ciia hinh chdp la a^

(b) Thd tich ciia hinh chdp la — a^

(c) Thd tich ciia hinh chdp la — a^ 6

(d) Ca ba cau tren ddu sai.

98

Cdu 3. Cho hinh chdp ddu ABCD canh a.

.,3

(a) Thd tfch ciia hinh chdp la a-V2

(b) Thd tfch ciia hinh chdp la

6

a'^

a V2 (c) Thd tfch cua hinh chdp la ;


Cdu 4. Cho hinh chdp tii giac ddu SABCD. Day ABCD la hinh vudng tam O canh

a. SO = a va vudng gdc vdi day

a (a) The tfch cua hinh chdp la — ;

6

( b , ™ . . . c h c . a h , „ h c h 6 p 4 ;

a^ (c) Thd tfch cua hinh chdp la — ;

(d) Ca ba cau tren ddu sai.

PhAN 2 . Bai tap tu luan 6 diem

Cau 5. (6 diem) Cho hinh chdp SABC. SA 1 AB, AB 1 AC, AC ± SA. Goij M, N

lin lugt la trung diem SB va SC.

a) Tfnh ti sd hai thd tfch ciia hinh chdp do mat phing AMN chia ra.

b) Cho SA = a, AB = 2a, AC = 3a. Tfnh khoang each tit A de'n mat phing (SBC).

De sd'2


Cdu I. Cho lang tru tam giac ABCA'B'C. Mat phing (AB'C) chia lang tru thanh

hai jAiin cd ti sd thd tfch la

99

(a) 1 ; (b) 2

(c) 3 ; (d) 4

Hay chgn cau tra ldi diing.

Cdu 2. Cho hinh lap phuang ABCDA'B'C'P' Mat phing (AB'D') chia hinh lap

phuang tranh hai phan cd ti sd the tfch la

(a) 3; (b) 4

(c) 5 ; (d) 6

Hay chgn cau tra ldi dung.

Cdu 3. Cho hinh chdp S.ABCD, day ABCD la hinh vudng eanh a. Mat phing

(SBD) chia binh chdp thanh hai phan cd ti le la :

(a) 1 ; (b) 2

(c) 3 (d)4

Hay chgn cau tra ldi diing.

Cdu 4. Cho hinh chdp SABCD day ABCD la hinh vudng canh a. Ggi M la trung

diem AB. Mat phing (SMD) chia hinh chdp thanh hai phan cd ti le la :

(a) 1 ; (b) 2

(c) 3 (d) 4

Hay chgn cau tra ldi diing

PhAN 2 . Bai tap tu luan 6 diem

Cau 5. (6 diem). Cho hinh chdp SABCD, day ABCD la hinh vudng canh a, tam O.

SA = a, SA vudng goc vdi day.

a) Tinh the tfch hinh chdp ASBC.

b) Tinh khoang each tii A de'n mp(SBC).

De sd'3


Hdy dien ddng sai vdo cdc khdng dinh sau:

Cdu 1. Cho binh chop SABCD, day ABCD la hinh vudng tam O, SO = a va vudng

gdc vdi day.

100

(a) JTmh chdp S.OAB cd the tfch la — 12

(b) Hinh chdp S.OAD ed the tfch la 12

,3

(c) Hinh chdp S.DAB cd thd tfch la

(d) ba khang dinh trdn ddu sai

Cdu 2. Cho hinh bat dien ddu SABCDS'

(a) Sd dinh ciia hinh bat dien la 5

(b) Sd canh cua hinh bat dien la 8

(c) Sd canh ciia hinh bat dien la 12

(d) Sd eanh ciia hinh bat dien la 24

Cdu 3. Cho hinh chdp S.ABCD.

D

D

D

•

• D n

(a) Ti sd thd tfch eua hai khdi chdp S.ABD va S.ABCD la - V] 2

(b) Tl sd thd tfch cua hai khdi chdp S.ACD va S.ABCD la - Fl 2 ^

(c) Ti sd thd tfch ciia hai khdi chdp S.CBD va S.ABCD la - Fl 2 ^

(d) Ca ba y tren ddu sai H

Cdu 4. Cho hinh lap phuang ABCDA'B'CD', day ABCD la hinh vudng canh a.

(a) Mat phang (CBD) chia khdi chdp thanh 2 phan ti Id la - [ ]

(b) Mat phing (CBD) chia khdi chdp thanh 2 phan ti Id la - \~\ 4

(c) Mat phing (CBD) chia khdi chdp thanh 2 phan ti le la - [ ]

101

(d) Ca ba y tren ddu sai P

PhAN 2. Bai tap tu luan 6 diem

Cau 5. (6 diem) Cho hinh chdp SABC, day ABCD la tam giac ddu canh a, G la

trgng tam cua tam giac ABC, SG _L (ABC).

a) Chung minh tam giac BSC la tam giac can.

b) Cho SA = a, tinh thd tfch khdi chdp.

HUONG D A N - DAP AN

De sd 1


Hdy chgn cdu trd ldi dung trong cdc cdu sau

Cdu 1

c

Cdu 2

a

Cdu 3

a

Cdu 4

b

PhAN 2. Bai tap tu luan 6 diem (HS tu giai)

De sd2


Cdu 1

b

Cdu 2

c

Cdu 2

a

Cdu 4

c


De sd 3


Cdu 1.

a

D

b

D

e

D

d

S

102

Cdu 2.

a

D

Cdu 3.

a

D

b

s

b

D

c

D

c

D

d

S

d

S

Cdu 4.

a

D

b

a'

c

S

d

S


Ban dgc tu giai.

103

Chi/dNq 2

MAT NON, MAT TRU, MAT CAU

P h a n 1

G\d\ THliu CHLfdNG

I. CAU TAO CHUONG

§ 1. Khai niem vd mat trdn xoay

§2 Mat ciu

On tap chuang II

1. Muc dich cua chuong

• Chuang II nhim cung cap cho hgc sinh nhiing kie'n thiic co ban vd khai nidm cac

khdi trdn xoay trong khdng gian ma chii ye'u la mat ndn, mat tru va mat ciu.

Mat ndn trdn xoay : Day, dudng sinh va dudng trdn day.

Dien tfch xung quanh va dien tich toan phin ciia mat ndn.

Thd tfch ciia khdi ndn trdn xoay

• Mat tru trdn xoay la gi ?

Didn tfch xung quanh va dien tfch toan phan eua mat tru.

The tfch ciia khdi tru trdn xoay

• Mat cau la gi ?

Didn tfch ciia mat ciu.

The tfch ciia khdi cau.

104

I I - MUC TIEU

1. Kien thufc

Nim dugc toan bd kien thiic ca ban trong chuong da neu tren.

- Hidu eac khai niem cac mat trdn xoay: Mat ndn, mat tru va mat cau.

Nim dugc eac cdng thitc tfnh didn tfch, thd tfch ciia cac khdi trdn xoay.

2. KI nang

TinK dugc didn tfch xung quanh, didn tfch toan phan ciia cac hinh trdn xoay.

Tinh dugc thd tfch ciia hinh tru, hinh ndn.

3. Thai do

Hgc xong chuang nay hgc sinh se lien he dugc vdi nhidu va'n dd thuc te sinh ddng, lien he duge vdi nhung vin dd hinh hgc da hgc d Idp dudi, md ra mdt each nhin mdi vd hinh hgc. Tii dd, cac em cd thd tu minh sang tao ra nhiing bai toan hoac nhirng dang toan mdi.

Kit ludn:

Khi hgc xong chuang nay hgc sinh cin lam tdt cac bai tap trong sach giao khda va lam dugc cae bai kidm tra trong chuang.

105

Phan 2,

ckc BAI SOAN

§1. Khai niem ve mat tron xoay

(tiet 1, 2, 3, 4, 5)

1. MUC Tl!U

1. Kien thufc

HS nim dugc:

1. Khai niem chung vd mat trdn xoay.

2. Hidu va van dung tfnh the tfch binh tru va binh ndn.

3. Dien tfch xung quanh va toan phin ciia mat tru va mat ndn.

2. KT nang

• Ve thanh thao cac mat tru va mat ndn.

• Tinh nhanh va chfnh xac didn tfch va the tfch hinh tru va hinh ndn.

• Phan chia mat tru va mat ndn bing mat phang.

3. Thai do

• Lien he dugc vdi nhidu van dd thue te trong khdng gian.


• Hiing thii trong hgc tap, tfch cue phat huy tfnh ddc lap trong hgc tap.

n. CHUAN DI CUA GV VA HS

1. Chuan bi cua GV:

• Hinh ve 2.1 de'n 2.12.

• Thudc ke, phin mau,...

106

2. Chuan bi ciia HS :

Dgc bai trudc d nha, cd thd lien he cac phep bie'n hinh da hgc d Idp dudi.

ra. PHAN DHOI TH6I LUONG

Bai dugc chia thanh 5 tiet:

Tiet 1: Tii dau de'n he't phan 1.

Tie't 2: Tie'p theo de'n he't muc 3 phin II

Tidt 3: Tie'p theo de'n he't phin II

Tie't 4: Tie'p theo de'n bet muc 3 phin III

Tie't 3: Tidp theo den bet phin III

IV. TlfN TDiNH DAY HOC

n. DAT VAN D€

Cau hdi 1.

Nhic lai khai nidm hinh ndn va hinh tru da hgc d cap 2.

Cau hdi 2.

Ndu mdt sd hinh ndn va hinh tru trong thuc te.

B. Biil MOI

HOATDQNGl

I. sir TAG THANH MAT TRON XOAY

GV neu cau hoi :

HI. Lg hoa thdng thudng ed phai mat trdn xoay hay khdng?

H2. Chie'c ndn Hue la mat trdn xoay?

107

• GV sir dung hinh 2.1 trong SGK va dat va'n dd:

H3. Hay dgc ten cac hinh d hinh 2.1.

H4. Em hinh dung dugc each lam lg hoa.

H5. Trong cac mat trdn xoay, cd mat nao chic chin la mat phing?

H6. Trong hinh 2.2, khi cit qua A mdt mat phing bat ki ta cd dugc dudng ^ hay

khdng?

H7. Ndu mdt sd hinh anh thuc te vd hinh tru va hinh ndn.

HOATDQNG 2

II. MAT NON TRON XOAY

1. Dinh nghla • GV eho HS tu phat bidu dinh nghia cua minh va sau dd kdt luan:

Trong mat phdng (P) cho hai dudng thdng d vd A cdt nhau tgi 0 tgo

thdnh gdc nhgn /?. Khi quay mat phdng xung quanh A thi dudng thdng d

sinh ra mdt mat trdn xoay vd dugc ggi Id mat ndn trdn xoay dinh 0

ngUdi ta thudng ggi tat la mat ndn. Dudng thang A ggi Id true, dudng

thdng d ggi Id dudng sinh, gdc 2/3 ggi Id gdc d dinh cua mat ndn dd.

Six dung hinh 2.3 va dat ra eac cau hdi:

H8. Phai chang mat ndn cd gidi ban bdi hai mat phang song song vdi nhau.

H9. Gdc giiia dudng sinh va true ludn ludn khdng ddi.

HIO. Cd mdt phep ddi xitng tam O bid'n mdi diem ciia mat ndn thanh mdi didm

ciia mat ndn.

2. Hinh ndn trdn xoay va khdi ndn tron xoay

• Sit dung hinh 2.4 va md ta:

108

• GV neu dinh nghia ;

Cho tam gidc vudng lOM. Khi quay nd xung quanh mgt cgnh gdc vudng

01 ta dugc mgt tgo thdnh mdt hinh dugc ggi Id hinh ndn trdn xoay. Ta

thudng ggi tdt Id hinh ndn.

• GV cd thd dat cau hdi:

HI 1. Hai tam giac lOM va lOM' ed bing nhau khdng?

HI2. Hay neu tap hgp didm ciia M.

• GV ndu tiep khai niem:

O ggi la dinh cua hinh ndn.

IM ggi la dudng sinh ciia hinh ndn

10 ggi Id dudng cao ciia hinh ndn

Tap hgp diemM la dudng trdn tdm I bdn kinh IM ggi Id ddy ciia hinh ndn.

Phdn hinh ndn bd di mat ddy ggi Id mat xung quanh cua hinh ndn.

H13.10 vudng gdc vdi day. Diing hay sai.

H14. Gdc tao bdi dudng sinh va dudng cao bing bao nhieu Ian gdc d dinh.

• GV ndu dinh nghia khdi ndn trdn xoay:

Khdi ndn trdn xoay Id phdn khdng gian gidi hgn bdi hinh ndn trdn xoay vd cd hinh ndn.

109

N la diem trong ne'u N thudc khd'i ndn.

N Id diem ngodi niu N khdng thugc khd'i ndn.

H15. Hay neu khai niem dinh, day, dudng sinh, dudng cao ciia khdi ndn.

3. Dien tich xung quanh cua hinh ndn trdn xoay

HI6. Hay ve mdt hinh chdp cd tat ca eac dinh cua day hinh chdp la da giac ndi tie'p

dudng trdn day cia hinh ndn. Dinh cua hinh chdp trimg vdi dinh ciia hinh ndn.

H17. Tam ciia da giac va tam ciia dudng trdn day ludn triing nhau. diing hay sai?

• GV ndu dinh nghla :

Dien tich xung quanh cua hinh ndn trdn xoay la gidi hgn cua dien tich

xung quanh cua hinh chdp deu ndi tiep hinh ndn dd khi sd cgnh ddy tdng

len vd hgn.

HI8. Didn tfch xung quanh ciia hinh chdp ddu ndi tie'p hinh ndn Idn ban hay nho

ban didn tfch xung quanh cua hinh ndn?

H19. Khi nao dien tfch hinh chdp va hinh ndn nhu tren triing nhau?

H20. Nhic lai cdng thiic tfnh dien tfch xung quanh cua hinh ndn.

• GV nhic lai cdng thiie : S = — pq trong dd q la khoang each tit O de'n mdt

canh p la chu vi day.

H21. Khi n ^^co thi p din de'n sd nao ?

• GV neu dinh If:

Dien tich xung quanh cua hinh ndn bdng nda chu vi ddy nhdn vdi do ddi

dudng sinh.

S^q=7ir/

no

• GV ndu tidp dinh nghla:

Tdng cua dien tich xung quanh vd dien tich ddy ggi Id dien tich todn phdn

cua hinh ndn.

4. The tich cua hinh ndn trdn xoay

• GV neu dinh nghia :

The tich cua hinh ndn trdn.xoay Id gidi hgn cua the tich cUa hinh chdp

diu ndi tie'p hinh ndn dd khi sd cgnh ddy tdng len vd hgn.

H22. Ndu cdng thiic tfnh the tfch hinh chdp.

GV nhic lai V f . = - B h . • ^ 3

H23. Khi sd eanh cua hinh chdp dan tdi cx) thi didn tfch day din de'n sd nao?

• GV ndu cdng thiic :

1 1 9 V„ - - B h ^ - T t r ^ h .

5. Vi du

•GV cho HS tdm tit vf du:

111

Cau a

Hoat ddng cua GV

Cdu hdi 1

Hay chi ra dudng sinh cua hinh

ndn.

Cdu hdi 2

Tfnh do dai dudng sinh.

Cdu hdi 3

Tinh chu vi day.

Cdu hdi 4

Tinh dien tfch xung quanh cua

hinh ndn.

Hoat ddng cua HS


Dudng smh la OM.


, „ , , IM 1 - OM = = 2a

sin 30°


p =2 Ttr = 2Tr.a.


, Sxq = nr\ = 2na^

caub

Hoat ddng ciia GV

Cdu hdi 1

Tfnh dien tfch day.

Cdu hdi 2

Tfnh dudng cao.

Cdu hdi 3

TinhV

Hoat ddng ciia HS


S = na^


OI = aV3


V - ^^^^'^ 3

Thuc hidn ^ 2 trong 4 phiit. S

112

Hoat ddng ciia GV

Cdu hdi 1

Tfnh chu vi niia dudng trdn ldn.

Cdu hdi 2

So sanh chu vi ciia dudng trdn

day va niia chu vi dudng trdn ldn.

Cdu hdi 3

Tfnh r.

Hoat ddng cua HS


Niia chu vi ciia dudng trdn ldn la chu

vi dudng trdn nhd va bing 27IT


Bang nhau.


13

Ta cd TTR = 270-. Tit dd r = — 2

HOAT DONG 3

IIL MAT TRU TRON XOAY

1. Djnh nghla

• GV sii dung hinh 2.8 va dat ra cac cau hdi:

113

H24. So sanh OM va O'M'

H25. So sanh OO' va MM'

H26. Hinh OO'M'M la hinh gi?

• GV neu dinh nghia:

Trong mat phdng (P) cho hai dudng thdng A vd I. song song vdi nhau,

cdch nhau mdt khodng r. Khi quay mat phdng (P) xung quanh A thi

dudng thdng I vgch ra mdt mat tru trdn xoay Ngudi ta thudng ggi tdt

mat tru trdn xoay Id mat tru. Dudng thdng A ggi la tru, dudng thdng I ggi

Id difdng sinh cua mat tru.

Hll. Hay lay mdt sd hinh anh thuc te vd mat tru trdn xoay.

2. Hinh tru trdn xoay

H28. Phai chang mat tru dugc gidi ban bdi hai mat phang song song?

GV neu nhan xet:

Khi ta cit mat tru bdi hai mat phing song song va vudng gdc vdi true thi ta dugc

mdt hinh try trdn xoay.

H29. Hay neu dinh nghia hinh tru trdn xoay.

a) Hinh tru trdn xoay

• GV neu dinh nghla:

Khi quay mdt hinh chit nhdt chung qugnh mot cgnh cua hinh chii nhdt do

ta dugc mdt hinh tru trdn xoay.

Cgnh diing de quay ggi la true.

Cgnh ddi dien ggi Id dudng sinh

Hai cgnh cdn lgi Id hai bdn kinh ddy cua hai mat ddy.

114

H30. Hai day cua hinh tru la hinh gi?

H31. Khi cit hinh tru bdi mdt mat phing song song vdi hai day ta dugc hinh gi?

H32. Khi cat hinh tru bdi mat phing di qua tmc ta dugc hmh gi?

H33. Hay md ta mat xung quanh cua mat tru.

H34. Hay ndu chidu cao cua hinh tru.

H35. So sanh dudng cao va dudng sinh.

H36. So sanh hai day.

b) Khdi tru trdn xoay

GV ndu cac khai niem:

- Khdi tru la gi ?

- Didm ngoai va didm trong eiia mat tru.

- Mat day, dudng sinh, dudng cao ciia khdi tru.

3. Dien tich xung quanh cua hinh tru trdn xoay

a) Hinh ldng tru ndi tie'p hinh tru:

115

• GV neu khai niem lang trii ndi tie'p hinh tru trdn xoay :

Mdt hinh ldng tru ggi Id ndi tie'p hinh tru niu hai ddy ciia hinh ldng tru

ngi tiip hai dudng trdn ddy ciia hinh tru.

H37. Neu mdt sd vf du vd hinh anh ciia dinh nghla trdn.

• GV neu dinh nghia :

Dien tich xung quanh mdt hinh tru trdn xoay Id gidi hgn cUa dien tich

xung quanh hinh ldng tru ndi tiep hinh tru dd khi sd'cgnh cua da gidc ddy

ddn ra vd cue.

b) Cdng thuc tinh dien tich xung quanh ciia hinh tru

H38. Hay nhic lai cdng thiie didn tfch xung quanh cua hinh lang tru.

H39. Hay nhic lai cdng thiic dien tfch xung quanh cua hinh lang tru ddu.

• GV nhic lai cdng thiic dien tfch xung quanh ciia hinh lang tru ddu :

Sj q = ph (p lachu vi day, h la dudng cao).

• GV neu dinh nghla :

116

Dim tich xung quanh cua hinh tru Id gidi hgn cua dien tich xung quanh

cua hinh ldng tru deu ndi tie'p hinh tru dd khi sd cgnh ddy cua ldng tru

ddn ra vd cue.

• GV ndu khai nidm dien tfch toan phin :

• GV neu hinh bieu didn didn tfch toan phin ciia mdt hinh tru:

H40. hay chi ra cac phin cd :

- Dd dai bang nhau .

Cd didn tfch bing nhau

d hai hinh trdn

4. The tich khdi tru trdn xoay

a) Dinh nghia:

The tich khdi tru trdn xoay la gidi hgn cua the tich khdi ldng tru diu ndi

tiep khdi tru dd khi cgnh ddy tdng len vd hgn.

117

b) Cdng thdc:

GV neu cdng thiic :

Thuc hien ^ 3 trong 4 phut.

V = Bh

A'

D' B'

C

Hoat ddng cua GV

Cdu hdi 1

Tfnh ban kfnh ciia dudng trdn day cua hinh tru

Cdu hdi 2

Tinh chu vi dudng trdn day.

Cdu hdi 3

Tfnh dien tich xung quanh.

Hoat ddng ciia HS


aV2 r =


p - IKX = 2n = Trav2 .


Sxq = Pl = 7taA/ .a = Tia^4i.

118

5. Vi du

GV cho HS neu tdm tit bai toan, ve hinh.

. /O

a

/

l^^-^ ' N k ^ ^ . - ^ 1 ji

— 1 - - 1 c 1 '' *^

y '''" y

cau a.

Hoat ddng cua GV

Cdu hdi I

Hay chi ra va tfnh ban kfnh day cua hinh tru.

Cdu hdi 2

Hay chi ra va tfnh dudng sinh cua hinh tru.

Cdu hdi 3

Tinh dien tfch xung quanh.

Hoat ddng cua HS


r = A I = ^ 2


I = AD = a.


Svn = p l = 27t —a = 7ca xq i- 2

Caub.

Hoat ddng cua GV

Cdu hdi I

Hay chi ra va tfnh ban kfnh day

ciia hinh tru.

Hoat ddng ciia HS


AT ^

r = AI = — 2

119

Cdu hdi 2

Hay cbl ra va tfnh dudng cao ciia

hinh tru.

Cdu hdi 3

Tinh thd tfch xung quanh.


h = IH = a.


V = Tir^h = Tt [ij

2 1 1 2

= —Tia 4

HOAT DONG 4

TOM TflT Bfll Hpc

1. Trong mat phang (P) cho hai dudng thing d va A cit nhau tai O tao thanh gdc

nhgn p. Khi quay mat phing xung quanh A thi dudng thing d sinh ra mdt mat trdn

xoay va dugc ggi la mat ndn trdn xoay dinh O ngudi ta thudng ggi tit la mat non.

Dudng thing A ggi la true, dudng thing d ggi la dudng sinh, gdc 2(3 ggi la gdc d

dinh cua mat ndn dd.

2. Cho tam giac vudng lOM. Khi quay nd xung quanh mdt canh gdc vudng 01 ta

tao thanh mdt hinh duge ggi la hinh ndn trdn xoay. Ta thudng ggi tit la hinh ndn.

O ggi la dinh ciia hinh ndn.

IM ggi la dudng sinh ciia hinh ndn.

IO ggi la dudng cao cua hinh ndn.

Tap hgp didm M la dudng trdn tam I ban kfnh IM ggi la day ciia hinh ndn.

Phan hinh ndn bd di mat day ggi la mat xung quanh cua hinh ndn.

3. Khdi ndn trdn xoay la phan khdng gian gidi ban bdi hinh ndn trdn xoay va ca

hinh ndn.

N la didm trong ne'u N thudc khdi ndn.

N la didm ngoai ne'u N khdng thugc khdi ndn.

120

4. Didn tfch xung quanh cua hinh ndn bing nua chu vi day nhan vdi do dai dudng

sinh. S q =: Tir/

5.Tdng cua dien tfch xung quanh va dien tfch day ggi la dien tfch toan phin cua

hinh ndn.

6. The tieh ciia hinh ndn trdn xoay la gidi ban cua thd tfch ciia hinh chdp ddu ndi

tidp hinh ndn dd khi sd canh day tang Ien vd ban.

1 1 9 V = - B h = -Ttr^h.

" 3 3

7. Trong mat phing (P) cho hai dudng thing A va 1. song song vdi nhau, cich nhau

mdt khoang r. Khi quay mat phang (P) xung quanh A thi dudng thing 1 vach ra

mdt mat true trdn xoay Ngudi ta thudng ggi tit mat tru trdn xoay la mat tru.

Dudng thing A ggi la true, dudng thing 1 ggi la dudng sinh ciia mat tru.

8. Khi quay mdt hinh chu: nhat chung quanh mdt eanh ciia hinh chii nhat dd ta

dugc mdt hinh tru trdn xoay.

Canh diing dd quay ggi la true.

Canh ddi didn ggi la dudng sinh

Hai canh cdn lai la hai ban kfnh day cua hai mat day.

9. Mdt hinh lang tru ggi la ndi tidp hinh tru nd'u hai day ciia hinh lang tru ndi tidp

hai dudng trdn day ciia hinh tru.

Didn tfch xung quanh mdt hinh tru trdn xoay la gidi ban eua dien tfch xung quanh

hinh lang tru ndi tie'p hinh tru dd khi sd canh ciia da giac day din ra vd cite.

10. Didn tfch xung quanh eiia hinh tru la gidi ban ciia dien tich xung quanh cua

hinh lang tru ddu ndi tie'p hinh tru dd khi sd eanh day ciia lang tru din ra vd cue.

S„„ = 27rr/ Aq

11. Didn tfch toan phin :

^tp - Sxq + S(j

12. Thd tfch khdi tru trdn xoay la gidi han eua thd tfch khdi lang tru ddu ndi tiep

khdi tru dd khi canh day tang Idn vd ban.

Cdng thiic : V = Bh

121

HOATDQNG 3

MQT SO CflU H6r TR^C NGHl|M

Hay didn diing (D) sai (S) vao cac khang dinh sau :

Cdu 1.

(a) Hinh ndn va hinh chdp la nhu nhau.

(b) Mat ndn trdn xoay va hinh ndn la nhu nhau.

(c) Hinh ndn la mdt phin ciia mat ndn.

(d) Ca ba khang dinh trdn ddu sai.

Trd ldi.

a

S

b

S

c

S

d

D

Cdu 2.

(a) Mat ndn trdn xoay la mdt hinh cd tam ddi xiing.

(b) Mat ndn trdn xoay khi bi cit bdi mdt mat phang vudng gdc vdi true

ta cd the duge mdt hinh ndn.

(e) Hinh ndn cd mdt true ddi xumg.


Trd ldi.

a

D

b

D

c

D

d

S

D D D •

D

D D n

122

Cdu 3.

(a) Mat tru trdn xoay khdng cd gidi ban. [_}

(b) Hinh tru cd gidi ban. U

(c) Khi cit mdt hinh tru bdi mdt mat phang // true ta dugc hinh chii nhat. [J

(d) Ca ba khing dinh trdn ddu sai. Ll

Trd ldi.

a

D

b

D

c

D

d

s

Cdu 4.

(a) Mat tru trdn xoay khi gidi han bdi hai mat phang

song song ta dugc hinh tru.

(b) Mat tru trdn xoay khi gidi han bdi hai mat phing

vudng gdc vdi true ta dugc hinh tru.

(c) Khi cit mdt hinh tru bdi mdt mat phang ± true ta dugc hinh trdn.


Trd ldi.

a

D

b

D

c

D

d

S

D

D • D

Chgn kh^ng djnh diing trong cac cau sau:

Cdu 5. Cho hinh chdp ndi tidp mdt hinh ndn

(a) Hai hinh chdp va hinh ndn cd dudng cao trung nhau;

(b) Thd tfch hinh chdp va thd tfch hinh ndn bing nhau.

(c) Thd tfch hinh chdp Idn ban the tfch hinh ndn.

(d) Ca ba y trdn ddu diing.

Trd ldi. (a).

Cdu 6. Cho hinh chdp luc giac ddu canh day la 2v3 ndi tidp mdt hinh ndn co dudng cao la 3.

S

Dudng cao ke tii S cua mdi mat bdn ciia hinh chdp la :

(a)2VlO; (b)Vio

10 (c)

Trdldi. (b).

(d)10

Cdu 7 Cho hinh chdp luc giac ddu canh day la 2>/3 ndi tidp mdt hinh ndn co dudng cao la 3.

124

Didn tfch xuhg quanh ciia hinh chdp la :

(a)6V30; (b) V30

(c)4V30; (d)5V30

Trdldi. (a).

Cdu 8. Cho hinh chdp luc giac ddu canh day la 2V3 ndi tidp mdt hinh ndn cd dudng cao la 3.

Ban kfnh dudng trdn day la:

(a) 2yf3;

,. 2V3 ( 0 — ;

Trdldi. (a).

(b) 2V6

(d) V3.

Cdu 9. Cho hinh chdp luc giac ddu canh day la 2V3 ndi tie'p mdt hinh ndn cd dudng cao la 3.

125

Dudng sinh la:

(a)2V3;

, - 2V3

(b) 2V6

(d) V3.

Trdldi. (b).

Cdu 10. Cho hinh chdp luc giac ddu canh day la 2>/3 ndi tiep mdt hinh ndn cd

dudng cao la 3.

(b) 24TIV2

(d) 48TI^/2

Didn tfch xung quanh cua hinh ndn la

(a) llnyfl;

(c) 6T1V2 ;

Trdldi. (d).

Cdu 11. Cho hinh chdp luc giac ddu canh day la 2>/3 ndi tidp mat hinh ndn cd

dudng cao la 3

126

Didn tfch toan phin ciia hinh ndn la:

(a) I2T1V2 + 1271;

(c) 6TiV2 + 127r;

Trdldi. (d).

Cdu 12. Cho hinh chdp luc giac ddu canh day la 2V3 ndi tie]

dudng cag la 3.

(b) 24TIV2 + 127I

(d) 4 8 T I ^ + 1 2 T I .

tiep mdt hinh ndn cd

Thd tfch ciia hinh ndn la:

(a) 1271; (b) 671

(c) 871; (d) IOTI.

Trdldi. (a).

Cdu 13. Cho hinh lang tru luc giac ddu eanh day la 2V3 ndi tie'p mdt hinh tru cd dudng cao la 3.

127

A'

, /-->

Didn tfch xung quanh ciia hinh lang tru la:

(a)36V3; (b) 16V3

(c)46V3; (d)26V3

Trd ldi. (a).

Cdu 14. Cho hinh lang tru luc giac ddu eanh day la 2V3 ndi tidp mdt hinh tru co dudng cao la 3.

A

A'

/

D' E'

Dudng sinh cua hinh tru la

(a)2V3;

(c)3;

Trd ldi. (c).

(b)3V3

(d)6.

128

Cdu 15. Cho hinh lang tru luc giac ddu canh day la 2V3 ndi tie'p mdt hinh tru cd dudng cao la 3.

B

, / ' - - - - - • ' - •

B'

->

D'

Ban kfnh day ciia hinh tru la:

(a)r = 2V3; (b)r = 3V3

(c) r = 3 ; (d) r = 6.

Trd ldi. (a).

Cdu 16. Cho hinh lang tru luc giac ddu canb day la 2V3 ndi tie'p mdt hinh tru cd dudng cao la 3

A

C

129

Dien tich xung quanh cua hinh tru la

(a)127tV3; (b) HTIVS

(c) 1271; (d) 1471.

Trd ldi. (a).

Cdu 17 Cho hinh lang tru luc giac ddu canh day la 2V3 ndi tiep mgt hinh tru co

dudng cao la 3.

A B

, ^-= H ^ '

C

E'

Dien tich toan phan ciia hinh tru la :

(a)127tV3; (b)207rV3

(c) 1271; (d) 1471.

Trdldi. (b).

Cdu 18. Cho hinh lang tru luc giac ddu canh day la 2v3 ndi tie'p mdt hinh tru co dudng cao la 3.

130

Thd tfch ciia hinh tru la :

(a)97tV3 ;

(c) 1271;

Trdldi. (a).

(b) 107tV3

(d) 1471.

HOAT DONG 6

m(ff\Q DflN Bfll T6P SGK

Bai 1. Hudng ddn. Six dung dinh nghia mat tru trdn xoay.

Cl _L

_ l I

131

Hoat ddng cua GV

Cdu hdi 1

Ggi O la tam dudng trdn, A la

dudng thing di qua tam 0 va A ± (P). m la dudng thing bat ki ai qua mdt diem thugc dudng trdn.

Tim mdi quan he cua m va A.

Cdu hdi 2

Chiing minh nhan dinh tren.

Cdu hdi 3

Tim true ciia mat tru.

Hoat ddng cua HS


m//A.

m each A mgt khoang khdng ddi.


Dua vao dinh nghla.


A chfnh la true.

Bai 2. Hudng ddn. Dua vao dinh nghia hinh tru, hinh ndn.

Ddp sd

a) Hinh tru

b) Hinh ndn

c) Khdi ndn.

d) Khdi tru

Bai 3. Hudng ddn. Dua vao tinh chat cua da didn va hinh lap phuang.

Hinh lap phuang cd 8 dinh va 6 mat.

Sd canh cua hinh lap phuang la 6.

132

cau a.

Hoat ddng cua GV

Cdu hdi I

Chi ra dudng cao h.

Cdu hdi 2

Cbl ra ban kfnh day.

Cdu hdi 3

Tam giac SOA cd dac didm gi ?

Cdu hdi 4

Tfnh dien tfch xung quanh ciia hinh ndn.

Hoat ddng cua HS


h = SO = 20cm


r = OA - OB = 25cm.


Tam giac SOA la tam giac vudng tai O. Tir dd ta cd dudng sinh

1 = Vl025


S,„ =27irl= 7T.25.V1025. Aq

caub.

Hoat ddng cua GV

Cdu hdi 1

Nhic lai cdng thiie tfnh V

Hoat ddng cua HS


V = - Tir h 3

133

Cdu hdi 2

TinhV


V = -n.25^.20 3

cau c.

Hoat ddng ciia GV

Cdu hdi 1

Tfnh OH

Cdu hdi 2

TfnhOI.

Cdu hdi 3

Tinhs SI.

Cdu hdi 4

Tfnh dien tfch thiet dien SAB.

Hoat ddng cua HS


OH = 12 em.


^ ^ 1 1 , 1

OH^ h^ lO^

Tif dd ta cd IO = 15em.


Dua vao tam giac vudng SOI ta cd

SI = 25em.


S = 500cm.

Bai 4. Hudng ddn. Dua vao dinh nghia hinh ndn. d

134

Hoat ddng cua GV

Cdu hdi 1

TInhBH

Cdu hdi 2

Ggi a = BAH, a cd dinh. Diing hay sai?

Cdu hdi 3

Chiing minh nhan dinh tren.

Hoat ddng cua HS


BH = 10cm


Diing. a = 30"


HS tu chung minh.

Bai 5. Hudng ddn. Dua vao dinh nghia hinh tru.

Cau a.

Hoat ddng ciia GV

Cdu hdi 1

Xac dinh dudng sinh 1.

Cdu hdi 2

Tinh didn tfch xung quanh.

Cdu hdi 3

Tinh thd tfch hinh tru

Hoat ddng cua HS


1 = OO' = 7cm.


S^q=2Tirl = 2Ti.5.7 = 707i


V-7 i r2h = 71.5^7 = 17571.

caub.

135

Hoat ddng cua GV

Cdu hdi 1

Tinh AB.

Cdu hdi 2

TInh dien tich thie't didn.

Hoat ddng ciia HS


Tacd AI^ =OA^-OI^ = 2 5 - 9 = 16.

Do dd AB = 2AI = 8cm


Std=AB.OO' = 56cm^

Bai 6. Hudng ddn. Dua vao dinh nghia hinh ndn va tfnh cha't eua hinh ndn. s

cau a.

Hoat ddng cua GV

Cdu hdi I

Xac dinh dudng sinh 1.

Cdu hdi 2

Xac dinh ban kfnh r.

Cdu hdi 3

Xac dinh dudng cao ciia hinh tru.

Cdu hdi 4

Tfnh dien tfch xung quanh eua hinh tru.

Hoat ddng cua HS


1 =SA = 2a.


r = OA = a


Dudng cao eiia hinh tru la :

SO= aV3


1 2 S„„ = — 27ta.2a = 2Tia xq 2

136

Cdu hdi 5

Tfnh thd tfch cua hinh tru.


na' N-—na h = —Tta .av3 3 3 3

^

Bai 7 Hudng ddn. Dua vao dinh nghla hinh tru, tfnh chat ciia hinh tru, dien tfch

xung quanh va the tfch hinh tru. A

, - -I r

^ — X u _

O'

B

cau a.

Hoat ddng ciia GV

Cdu hdi I

Tinh didn tfch xung quanh ciia hinh tru.

Cdu hdi 2

Imh dial tfch toan phin eiia hinh tru.

Hoat ddng cua HS


S„- = 2TirI - 2Tir.rv3 = 2v3Tir Aq


S,p=S,q+2Sd=2( l + V3)Tir2

caub.

Hoat ddng ciia GV

Cdu hdi I

Nhic lai cdng thiic tfnh thd tfch hinh tru.

Cdu hdi 2

TfnhV

Hoat ddng cua HS


V = Ttr^h.


V = Trr h = Ttr^rV3=Tir^V3

137

cauc.

Hoat ddng cua GV

Cdu hdi 1

Xac dinh true ciia hinh tru.

Cdu hdi 2

Ke AA' // OO' xac dinh mdl quan he giira 0 0 ' va mp(AA'B)

Cdu hdi 3

Xac dinh khoang each giira OO'

vaAB.

Cdu hdi 4

Tfnh gdc A ^

Cdu hdi 5

Tfnh BA' va O'H

Hoat ddng cua HS


OO'


OO' // (AA'B)


La khoang each giiia 0 0 ' va

mp(AA'B). Ke O'H 1 A'B. OH ehfnh la khoang each dd.


A ^ =30°


BA = AA'tan30'^ = rV3 . -7 i— . V3=r

x/3 A BA'O' ddu ndn O' H = ^ ^

2

Bai 8 Hudng ddn. Dua vao dinh nghla, tfnh chit, didn tfch xung quanh va thd tfch

hinh tru va hinh ndn.

A O"

/ / / / /.y—[-

r / do M

138

caua.

Hoat ddng ciia GV

Cdu hdi I

Tfnh dien tfch xung quanh ciia hinh tru.

Cdu hdi 2

Dd tfnh didn tfch xung quanh ciia hinh ndn ta cin tfnh gi.

Cdu hdi 3

Tinh didn tfch xung quanh eiia hinh ndn.

Cdu hdi 4

Tfnh ti sd hai didn tfch dd.

Hoat ddng ciia HS


Sxq(T) = 27ir.rV3 = 2^T^


Can tfnh O'M.

Tacd 0 ' M = V00'2 + 0M^ -


Sxq(N) = "rl = 27tr^


S x q ( T ) ^ ^

Sxq(N)

= 2r

caub.

Hoat ddng ciia GV

Cdu hdi 1

Thd tfch khdi ndn bing bao nhidu phin thd tfch khdi tru.

Cdu hdi 2

Thd tfch phin cdn lai bing bao nhidu thd tfch khdi tru.

Cdu hdi 3

Tinh ti sd hai thd tfch dd.

Hoat ddng ciia HS


V ) = 3 (T)


2


V) 1 V(CL) 2

139

Bai 9 Hudng ddn. Dufa vao dinh nghla, tfnh cha't, dien tfch xung quanh va the tfch

hinh tru va hinh ndn.

cau a.

Hoat ddng ciia GV

Cdu hdi I

Gia sii khi cit hinh ndn ta dugc tam giac SAB. Xac dinh gdc vudng va dd dai cae canh.

Cdu hdi 2

Tfnh ban kfnh dudng trdn day.

Cdu hdi 3

Tfnh chidu cao ciia hinh chdp.

Cdu hdi 4

Xac dinh dudng sinh.

Cdu hdi 5

Tfnh didn tfch xung quanh.

Hoat ddng ciia HS


Gdc vudng la gdc ASB, SA = av 2


r A aV2 r = OA =

2


h = S O = ^ ^ 2


1 = SA = a.


aV2 TtV2a2 S„„ =7irl = 7 t ^ — . a =

xq 2 2

140

Cdu hdi 6

Tfnh didn tfch day.

Cdu hdi 7

Tfnh the tfch hinh ndn..


2 Tta S . = Tir =

'' 2 Ggi y trd ldi cdu hdi 7

1 7, •V2TI T VN =-Tir^h = -^—a^

^ 3 12

caub.

Hoat ddng cua GV

Cdu hdi 1

Xac dinh a i O

Cdu hdi 2

TfnhBH

Cdu hdi 3

Tfnh dien tfch tam giac SBC.

Hoat ddng cua HS


SH6 = 6O°


BH= VSB -SH^ = 4 -V3


S = S H . B H = ^ ' ' ^ 3

Bai 10 Hudng ddn. Dua vao dinh nghla, tfnh chat, dien tfch xung quanh va thd tfch

hinh tru va hinh ndn. D

A ' - - -« 1 - -

^ ma

141

cau a.

Hoat ddng cua GV

Cdu hdi I

ABCD' la hinh gi?

Cdu hdi 2

Tfnh A C

Cdu hdi 3

TfnhAB

Cdu hdi 4

Tfnh dien tfch hinh vudng ABCD.

Cdu hdi 5

Tfnh didn tfch hinh vudng ABCD'

Cdu hdi 6

Tfnh cosa.

Hoat ddng cua HS


Hinh chii nhat


A C = 2r.


Tacd

BC'^ = AC^ - AB^ - 4r2 - AB^

BC'2 = BC^ - CC '2 = AB^ - r^

x ^ ^ ' » ' AB rVio Tu do ta CO AB = .

2 Goi y trd ldi cdu hdi 4

s=y 2



cosa = ^^c'^' = I-SABCD ^5

(1)

(2)

142

MOT SO CAU HOI ON TAP HOC Kl 1 > > •

Hdy dien dung, sai vdo cdc d trdng sau ddy md em cho Id hgp li nhdt.

Cdu 1. Cho hinh chdp S.ABCD, day ABCD la hinh vudng canh a, SA = a

SA l(ABCD).

(a) Thd tfch hinh chdp la a'

(b) Thd tfch hinh chdp la — a'

1 ,

(c) Thd tfch hinh chdp la — a


Trd ldi.

a

S

b

D

c

S

d

S

n D

D

D

Cdu 2. Cho hinh hop chii nhat ABCDA'B'CD' cd AA' = c, AB = a, AD = b

B' C

A' y^ 1 D

y B y^


(b) Thd tfch hinh chdp A'.ABCD la abc

(c) The tfch hinh chdp A'.ABCD la - abc

(•^^ ^ (ABCD.A 'B 'CD' ) ^ - ^ ^ ( A ' . A B C D )

Trd ldi.

a

D

b

S

e

D

d

D

•

• D

Cdu 3. Cho hinh hop ehii nhat ABCDA'B'CD' cd 3 canh la a, b, c. B' C

^y 1 D > ^

.y ^ y^


(b) Thd tfch hinh chdp A'.ABD la abc

(c) Thd tfch hinh chdp A'.ABD la - abc

D D

D

144

^^)'^(ABCD.A'B'CD') = 6 ^ ( A ' . A B D )

Trd ldi.

D

a

D

b

S

c

D

d

D

Cdu 4. Cho hinh chdp S.ABCD, day ABCD la hinh vudng canh, SA = a vudng gdc vdi day.

S

(a) SB = aV2

(b) SD = ayf2

(c) Didn tfch tam giac SBD bing


Trd ldi.

a^S

a

D

b

D

c

D

d

S

D D

D

D

145

Cdu 5. Cho hinh lap phuang ABCDA'B'CD' canh a.

/ \

A' 1

/ B

/ /

/ r

D'

(a) Thd tfch khdi lap phuang la a'

(b) Thd tich khdi chdp A'.ABCD la -a^

(c) Thd tich khdi lang tru ABDA'B'D' la -a^ 6

(d) Ca ba cau tren ddu sai

Trd ldi.

a

D

b

D

c

S

d

S

• D

D

D



SA l(ABCD), SA = a, AB = 2a, AD = DC = a. Khoang each tur B de'n (SAD) la

146

(a) a ; (b) 2a

(c) ayfs ; (d)aV2

Trd ldi. (b).


SA J.(ABCD), SA = a, AB = 2a, AD = DC = a. Thd tfch khdi chdp la

(a) (b)

(c) (d) Ca ba cau trdn ddu sai.

Trd ldi. (a).


SA ±(ABCD), SA = a, AB = 2a, AD = DC = a. The tfch khdi chdp S.ABC la

(a)

-f (d) Ca ba cau trdn ddu sai.

Trd ldi (b).


SA ±(ABCD), SA = a, AB = 2a, AD = DC = a. Khoang each giiia SA va BC la:

148

(a) a ;

(c) aV2 ;

(b)2a

2a Ve

Trdldi (d).

Cdu 10. Cho hinh chop SABCD, day ABCD la hinh thang vudng tai A,

SA l(ABCD), SA = a, AB = 2a, AD = DC = a. Dien tfch tam giac SBC la:

S

(d)-• ^

(a) a^;

(c) a^yfl ; z

Trd ldi. (d).


SA = a. Khoang each giiia AB va SD la:

149

(a) a;

(c) aV2 ;

Trd ldi (d).

Cdu 12. Cho hinh chdp SABCD, day ABCD la hinh vudng tam O canh a,

SA l(ABCD), SA = a. Khi dd SO bing

(a) a;

(c) aV2 ;

Trd ldi. (d).

150

Cdu 13. Cho hinh chdp ndi tie'p mdt hinh ndn

(a) Hai hinh chdp va hinh ndn cd dudng cao trung nhau;

(b) Thd tfch hinh chdp va thd tfch hinh ndn bing nhau.

(c) Thd tfch hinh chop ldn hon thd tfch hinh ndn.

(d) Ca ba y trdn ddu diing.

Trd ldi. (a).

Cdu 14. Cho hinh chdp luc giac ddu canh day la 2v3 ndi tie'p mdt hinh ndn cd

dudng cao la 3.

Dudng cao ke tit S cua mdi mat ben eiia hinh chdp la :

(a)2VlO; (b)VIo

VlO (c) (d)10

Trdldi. (b).

151

Cdu 15. Cho hinh chdp luc giac ddu eanh day la 2\f3 ndi tid'p mdt hinh ndn cd dudng cao la 3.

Didn tfch xung quanh ciia hinh chdp la :

(a)6V30; (b) VSO

(c)4V30; (d)5V30.

Trd ldi. (a).


8

Ban kfnh dudng trdn day la:

(a) 2V3;

, - 2V3 ( 0 — ; Trd ldi. (a).

(b) 2V6

(d)yf3

152


S

Dudng sinh la:

(a) 2V3;

, , 2V3 ( 0 — ; Trdldi. (b).

(b) 2V6

(d) V3

Cdu 18. Cho hinh chdp luc giac ddu canh day la 2V3 ndi tiep mdt hinh ndn cd dudng cao la 3.

S

Didn tfch xung quanh ciia hinh ndn la

(a) 127tV2; (b) 24TtV2

153

(c) 671V2 ; (d) 487TV2

Trdldi. (d).

Cdu 11. Cho hinh chop luc giac ddu canh day la 2V3 ndi tie'p mdt hinh ndn cd

dudng cao la 3.

Dien tfch toan phin cua hinh ndn la:

(a) I271V2 + 1271;

(c) 6TtV2 + 12Tt;

Trdldi. (d).

Cdu 19. Cho hinh chdp luc giac ddu canh day la 2V3 ndi tiep mdt hinh ndn cd

dudng cao la 3.

(b) 24TiV2 + 127t

(d) 487rV2 + 127i.

154

The tfch cua hinh ndn la:

(a) 1271;

(c) 871;

Trd ldi. (a).

(b)67t

(d) 1071.

Cdu 20. Cho hinh lang tru luc giac ddu canh day la 2V3 ndi tidp mdt hinh tru cd dudng cao la 3.

8

Didn tfch xung quanh ciia hinh lang tru la la:

(a)36V3; (b) 16V3

(c)46V3; (d)26V3

Trdldi. (a).

Cdu 21. Cho hinh lang tru luc giac ddu canh day la 2V3 ndi tie'p mdt hinh tru cd

dudng cao la 3.

155

A'

p

B'

- >

D' E

Dudng sinh ciia hinh tru la :

(a)2V3; (b)3V3

(c) 3 ; (d) 6.

Trd ldi. (c).

Cdu 22. Cho hinh lang tru luc giac ddu canh day la 2V3 ndi tidp mdt hinh tru cd dudng cao la 3.

B

" C

B' ..^-

•~~y

F D' E'

156

Ban kfnh day eua hinh tru la :

(a)r = 2V3; (b)r = 3V3

(c)r = 3 ; (d)r = 6.

Trdldi. (a).

Cdu 23. Cho hinh lang tru Itic giac ddu canh day la 2V3 ndi tie'p mdt hinh tru cd

dudng cao la 3.

A ^ _ _ _ ^ , _ _

C

Didn tfch xung quanh ciia hinh tru la

(a)127tV3; (b) 147tV3

(c) 1271; (d) 1471.

Trdldi. (a).

Cdu 24. Cho hinh lang tru luc giac ddu canh day la 2\G ndi tiep mdt hinh tru cd

dudng cao la 3

157

Didn tfch toan phin ciia hinh tru la

(a) 1 iTiS ;

(c) 127C;

Trdldi. (b).

(b)207tV3

(d) 1471.

158

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On tap chuang 1 64

Cftu-ong 2-MAT NON, MAT TRU, MAT CAU 104

P/ia/i i - GIOI THifiU CHUONG 104

PMn 2 - CAC BAI SOAN 106

§1. Khai niem ve mdt tron xoa\; 106

Mgt so cdu hoi on tap hgc ki 1 143

159

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Chiu trdch nhiem xudt bdn .

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