A colleague Bill Wardlaw (March 3, 1936-January 2, 2013) used to create a “Problem of the Week” for his students, giving a prize of a cookie if they could solve it. Here is one of them.

Mathematics Problem, #154

Find the volume of the intersection of three cylinders, each of radius a, which are centered on the x-axis, the y-axis, and the z-axis. That is, find the volume of the three dimensional region

E = {(x,y,z) | x² + y² < a², y² + z² < a², z² + x² < a²}.