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math

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2 planes parallel to the base of a pyramid cut the pyramid at 1/4 and 2/3 of the height as measured from the base up. If the volume of the pyramid is 100 cubic inches, what is the volume of the middle piece to the nearest tenth?

  • math - ,

    Volumes of pyramids above the cutting planes are proportional to the cube of the height.

    So the volume above the cutting plane at h/4 is
    V1=(3/4)^3*100=2700/64 in³
    Volume above the 2h/3 cut is
    V2=(1/3)^3*100=100/27 in³
    The volume between two cuts are therefore
    = V1-V2
    =100(27/64-1/27)
    =16625/432
    =38.48 in³ (approx.)

  • math - ,

    Thank you very much!

  • math :) - ,

    You're welcome!

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