Question

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?

Answer 1

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.)

Answer 2

Thank you very much!

Answer 3

You're welcome!