53 - 55 Solved Problems in Maxima and Minima

Problem 53
Cut the largest possible rectangle from a circular quadrant, as shown in Fig. 40.

Problem 54
A cylindrical tin boiler, open at the top, has a copper bottom. If sheet copper is m times as expensive as tin, per unit area, find the most economical proportions.

Problem 55
Solve Problem 54 above if the boiler is to have a tin cover. Deduce the answer directly from the solution of Problem 54.