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).