Napkin ring problem

If a hole of height is drilled straight through the center of a sphere, the volume of the remaining band does not depend on the size of the sphere. For a larger sphere, the band will be thinner but longer.
Animation of a cut napkin ring with constant height

In geometry, the napkin-ring problem involves finding the volume of a "band" of specified height around a sphere, i.e. the part that remains after a hole in the shape of a circular cylinder is drilled through the center of the sphere. It is a counterintuitive fact that this volume does not depend on the original sphere's radius but only on the resulting band's height.

The problem is so called because after removing a cylinder from the sphere, the remaining band resembles the shape of a napkin ring.