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

Explanation

To show that the height \( h \) of a closed right circular cylinder of given surface area \( A \) and maximum volume \( V \) is equal to the diameter of its 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
- \( A \) = total surface area of the cylinder
- \( V \) = volume of the cylinder
...