A classic problem from Calculus I is to take a wire of length L and cut it into pieces. One piece is bent into a circle and the remainder is bent into a square.
(a) Determine how the wire should be cut so the maximum area is enclosed by the two shapes. In particular, how much of the wire is used for the circle and how much is used for the square?
(b) How much area is enclosed in the square?
(c) How much area is enclosed in the circle?
(d) What is the maximum enclosed area?