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 of a closed right circular cylinder of given surface area and maximum volume is equal to the diameter of its base, we will 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

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