*Problem #50*

A standard problem from Calculus is to find the volume of the solid
*S* constructed as follows. The base of *S* is a circular disk
of radius 1. Parallel cross-sections perpendicular to the base are
squares. The first figure shows some of the cross-sections of *S*,
the second shows *S* itself. This solid is sometimes called a
"Bishop's Hat".
This month's problem is to find the surface area of the Bishop's Hat (do
not include the area of the circular base).