Napkin ring problem

In geometry, the napkin-ring problem involves finding the volume of what remains after a circular hole is drilled through a sphere. Specifically, the hole has the shape of a right circular cylinder (with two spherical caps) whose axis goes through the center of the sphere. Removing the "hole" leaves a circular "band". 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 the part that remains resembles the shape of a napkin ring.