Cylinder is inscribed in a sphere of radius .
What is the biggest volume of cylinder then?Code:* * * * - - - - - * * | | * * | | * | | * | | * * | * | * * | : \ | * | h: \R | * | : \ | * * | : r \| * * - - + - - * * * *
The radius of the cylinder is .
The height of the cylinder is .
The volume of the cylinder is: . 
In the diagram, we see that: . 
Substitute  into : .
Therefore, we must maximize: .
. . Go for it!