58 - 59 Maxima and minima: cylinder surmounted by hemisphere and cylinder surmounted by cone

Problem 58
For the silo of Problem 57, find the most economical proportions, if the floor is twice as expensive as the walls, per unit area, and the roof is three times as expensive as the walls, per unit area.

Solution:

 

Problem 59
An oil can consists of a cylinder surmounted by a cone. If the diameter of the cone is five-sixths of its height, find the most economical proportions.

Solution:

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