Given a sphere with radius r, a cone with radius r and height 2r, and a cylinder with radius r and height 2r, the sum of the volume of the cone and sphere is equal to the volume of the cylinder. If we look at the volume formulas, this is obvious. However, any ordinary person without mathematical training probably wouldn't find this intuitive.
I recall reading in a museum exhibit that before proving anything, Archimedes was able to slice up the sphere and cone and fit the pieces together into the cylinder--all in his mind. Can someone explain how one can slice up the shapes to do that?