(856,#21) Use polar coordinates to find the volume of the solid inside both the cylinder x² + y² = 4 and the ellipsoid 4 x² + 4 y² + z² = 64..

The Geometry
The top half of the solid under consideration looks like this:

There is a symmetric bottom half. The top half has the circle of radius 2 in the x-y plane as its base. So, the total volume is given by

by:sh