Szabályos hatoldalú gúla felszíne, térfogata, síkmetszete és átlós metszete

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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

    =

    =

    =

    =