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) | x^{2} + y^{2} __<__ *a*^{2}, y^{2} + z^{2} __<__ *a*^{2}, z^{2} + x^{2} __<__ *a*^{2}}.