Maximum Cylinder that can be Inscribed in a Sphere

Problem:

Using the AM-GM inequality, what is the maximum volume of a right circular cylinder that can be inscribed in a sphere of radius R.   We can argue easily that such a cylinder exists. 

Note: No calculus for this solution. Obviously it is a routine calculus problem.

One Solution.   (After you have tried . . .)

 

 

 

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