Unizor - Geometry3D - Pyramids - Problem 3
Channel: Zor Shekhtman on UNIZOR Education
Date: 30/09/2015

Unizor - Creative Minds through Art of Mathematics - Math4Teens

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Pyramids - Problem 3

Given a triangular pyramid SABC. A point on each side edge is chosen as follows.
Point A' divides edge SA so that AA'/A'S = ka
Point B' divides edge SB so that BB'/B'S = kb
Point C' divides edge SC so that CC'/C'S = kc
In what ratio does a plane that contains these three division points divide the volume of a pyramid?

Answer:

The ratio of the volume of the bottom part (unevenly truncated pyramid) to the volume of the top part (pyramid with side edges shorter than original) is
(1+ka)·(1+kb)·(1+kc) − 1