A classic problem from Calculus I is to take a wire of length L and cut it into two pieces. One piece is bent into a circular shape and the remainder...

A classic problem from Calculus I is to take a wire of length L and cut it into two pieces. One pieceis bent into a circular shape and the remainder is bent into a square shape.(a) Determine how the wire should be cut so the maximum area is enclosed. In particular, howmuch of the wire is used for the square, and how much is used for the circle?(b) How much area is enclosed in the square?(c) How much area is enclosed in the circle?(d) What is the maximum total enclosed area?Note: although this can be worked using Calculus I concepts, work this out using Calculus IIIconcepts.