Wednesday, September 30, 2015
Unizor - Geometry3D - Pyramids - Problem 3
Unizor - Creative Minds through Art of Mathematics - Math4Teens
To effectively learn from problem solving, try to solve these problems just by yourself, then listen to a lecture and then try to solve them again by yourself.
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?
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