Cavalieri's Principle

This 3-D model is composed of a base with two posts on it, one straight up and the other at a slant. The other components include two sets of circular rings, one set of 10 with height of 4mm and another set of 5 with height 8mm. The manipulative is used to demonstrate Cavalieri's principle, which states that when two objects have equal height and are divided into sections by planes parallel to and equal distance from the base, if those sections have equal volumes, than the total volume of the two objects are equal. With one post being slanted, we thought it best to divide one of the stacks of rings more than the other, and after printing found that the 8mm rings wouldn't quite sit flush with the base. So, the thinner rings need to be used on the slanted post. This does deviate slightly from the principle, but because the thinner discs have half the height of the thicker discs you can explain how a pair of the 4mm discs should be compared to a single 8mm disc.

B. Cook and W. Garske