Show that the right circular cylinder of given surface and maximum volume is such that its height is equal to the diameter of the base.

Explanation

To show that the right circular cylinder of given surface area has maximum volume when its height is equal to the diameter of the base, we can follow these steps:

### Step 1: Define the Variables
Let:
- \( r \) = radius of the base of the cylinder
- \( h \) = height of the cylinder
- \( S \) = surface area of the cylinder

...