TITLE: Given a solid sphere of radius R, remove a cylinder whose central axis goes through the center of the sphere.
QUESTION [7 upvotes]: Given a solid sphere of radius R, remove a cylinder whose central axis goes through
the center of the sphere. Let h denote the height of the remaining solid. Calculate the
volume of the remaining solid.

REPLY [4 votes]: There's a Wikipedia article about this problem: http://en.wikipedia.org/wiki/Napkin_ring_problem
It is solved neatly via Cavalieri's principle.
(Both of these Wikipedia articles were initially created by me.)