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Szabályos hatoldalú gúla felszíne, térfogata, síkmetszete és átlós metszete - kidolgozott feladatok
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SZABLYOS HATOLDAL GLA FELSZN, TRFOGAT, SKMETSZET S TLS METSZET KISZMTSA SAMU MIHLY LTALNOS ISKOLA PTERRVE
IV. SZABLYOS HATOLDAL GLA
31. Szmtsd ki a gla felsznt, ha testmagassga 12 dm, oldalle pedig 20 dm. 32. Szmtsd ki a gla F,V s tls s skmetszetnek terlett ha alaple 6 cm, egy oldallapjnak a terlete pedig 18 cm2
33. Szmtsd ki a gla trfogatt,ha alaple a=4 cm, oldalle pedig az alappal 45-os szget zr be
34. Szmtsd ki a gla felsznt s trfogatt ha alaple 6 cm, oldalle pedig 35 cm.
35. Szmtsd ki a gla felsznt, ha az alapba rhat kr sugara 6 cm, az oldallap s az alap kztti szg pedig 45
------------
?a?Pt?At ?F
dm 20sdm, 12ha
==
==
=
=
2562a
1444002a
4412a400
122a20
h2a
s
2
2
2
22
2
2a
22
=
=
+
=
+
=
+
=
2
2
dm 31536At 33286At
4332326At
43a6At
=
=
=
=
2
a
dm 1152Pt12323Pt
ha3Pt
=
=
=
cm 36h3ah
=
=
dm 32a216a
162a
2562a
2
=
=
=
=
cm 12d62da2d
2
2
2
=
=
=
ha
s s
a 2
a 2
OLDALA 2dm 3)3(4 384Ft115231536F
PtAtF
+=
+=
+=
------------
?h ?Ts?d ?Td ?V ?H??haPt?At ?F
cm 18Tcm, 6a
2
2
==
==
==
==
==
=
=
ha
s s
a 2
a 2
OLDALA cm 6h3:18h
h3182h618
2haT
a
a
a
a
a
=
=
=
=
=
H
ha ha
h 2
h 2
SKMETSZET
3cmH9H
2736HH2736
H2
366
H2hh
2
2
2
2
2
2
22
2a
=
=
=
+=
+
=
+
=
2
2
cm 354At 396At
43366At
43a6At
=
=
=
=
2
a
cm 108Pt663Ptha3Pt
=
=
=
2cm 2)354(F108354F
PtAtF
+=
+=
+=
3cm 354V3
3354V
3HAtV
=
=
=
2
2
cm18Td2
312Td
2HdTd
=
=
=
2cm39Ts2
336Ts
2HhTs
=
=
=
------------
?At ?V ?H
454cm,a
=
==
=
=
H
s s
d2 2
d2 2
TLS METSZET a
H
cm 4aH ==
2
2
cm 324At 346At
43166At
43a6At
=
=
=
=
3cm 332V3
4324V
3HAtV
=
=
=
------------
?V ?H?ha ?Pt
?At ?Fcm 53s
cm, 6a
==
==
==
=
=
ha
s s
a 2
a 2
OLDALA
( )
cm 6h36h
945hh945
h353
h2a
s
a
2a
2a
2a
2a
22
2a
22
=
=
=
+=
+=
+
=
2
2
cm 354At 396At
43366At
43a6At
=
=
=
=
2
a
cm 108Pt663Ptha3Pt
=
=
=
2cm 2)354(F108354F
PtAtF
+=
+=
+= 3cm 354V3
3354V
3HAtV
=
=
=
H
s s
d2 2
d2 2
TLS METSZET
( )
cm 3H9H
3645HH3645
H653
Has
2
2
2
222
222
=
=
=
+=
+=
+=
------------
?H ?h?ha ?Pt
?a ?F45
cm, 6r
==
==
==
=
=
cm 34a3
312a
33
312
a
3a12
2 /2
3a6
23a
r
=
=
=
=
=
=
cm 12h62hr2h
=
=
=
H
ha ha
h 2
h 2
SKMETSZET
r
H
cm 6HrH
=
= cm 26h
236h
72h3636h66hHrh
a
2a
2a
2a
222a
222a
=
=
=
+=
+=
+=
( )
2
2
2
cm 372At 3346At
433166At
43346At
43a6At
=
=
=
=
=
2
a
cm 672Pt26343Pt
ha3Pt
=
=
=
2cm )2(1372F2372372F
PtAtF
+=
+=
+= 3cm 3144V3
6372V
3HAtV
=
=
=
SZABLYOS HATOLDAL GLA FELSZN, TRFOGAT, SKMETSZET S TLS METSZET KISZMTSA SAMU MIHLY LTALNOS ISKOLA PTERRVE
36. Szmtsd ki a gla felsznt s tlsmetszetnek terlett ha =8 cm s s=12 cm 37. Szmtsd ki a gla felsznt s trfogatt ha oldalmagassga 13 cm, testmagassga 12 cm
------------
?H ?Td ?d
?ha ?Pt?At ?F
12cmscm, 8a
2
=
==
==
==
=
=
ha
s s
a 2
a 2
OLDALA
cm 28h
264h
128h
16144hh16144h412
h2a
s
a
a
2a
2a
2a
2a
22
2a
22
=
=
=
=
+=
+=
+
=
H
s s
d2 2
d2 2
TLS METSZET
cm 54H516H
80H
80144HH64144H812
Has
2
2
2
222
222
=
=
=
=
+=
+=
+=
2
2
cm 396At 3166At
43646At
43a6At
=
=
=
=
2
a
cm 2192Pt2883Pt
ha3Pt
=
=
=
2cm )223(96F2192396F
PtAtF
+=
+=
+=
cm 16d82d
2ad
2
2
2
=
=
=
2
2
cm 532Td2
5416Td
2HdTd
=
=
=
----------
?V ?a?h ?Pt?At ?F
cm 12Hcm, 13ha
==
==
==
=
=
H
ha ha
h 2
h 2
SKMETSZET
252h
1441692h
1442h169
122h13
H2hh
2
2
2
22
2
22
2a
=
=
+
=
+
=
+
=
cm 10h52h
52h
252h 2
=
=
=
=
cm 3
310a
33
310
a
3a103ah
=
=
=
=
2
2
2
cm 350At3252At
43
931006At
43
33106At
43a6At
=
=
=
=
=
2
a
cm 3130Pt
133
3103Pt
ha3Pt
=
=
=
2cm 3180F3130350F
PtAtF
=
+=
+=
3cm 3200V4350V
312350V
3HAtV
=
=
=
=