Sphere = Cylinder - Cone

image

The Sphere has volume (4/3)πr^3, the Cylinder has volume πr^3, and the cones have combined volume (2/3)πr^3. Here is an illustration of how the sphere deforms into a cylinder, leaving a cone-shaped hole in the middle. This animation was inspired by a talk that Dan Finkel once gave.

(Mathematica Notebook)