Cavalieri's Principle
- Author:
- Mike May, David Chandler
Cavalieri's Principle states that if two or more objects have the same height and parallel cross sections at any level have the same area, then the objects have the same volume. One application of this is to extend the formula for the volume of a pyramid from triangular based pyramids (which can be derived directly by dissection), to pyramids with any shape base. The volume of a triangular based pyramid is
V = 1/3 A(base)*height.
Since a pyramid of any base shape can be paired with a triangular base pyramid, and since it can be shown that the parallel cross sections at any height have equal area, the volume formula applies regardless of the shape of the base.