29 - 31 Solved problems in maxima and minima

Problem 29
The sum of the length and girth of a container of square cross section is a inches. Find the maximum volume.

Solution:

 

Problem 30
Find the proportion of the circular cylinder of largest volume that can be inscribed in a given sphere.

Solution:

 

Problem 31
In Problem 30 above, find the shape of the circular cylinder if its convex surface area is to be a maximum.

Solution:

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