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

Largest rectangle inscribed in a circular quadrant

 

Solution:

 

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.

Solution:

 

Problem 55
Solve Problem 54 above if the boiler is to have a tin cover.

Solution:

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