The volume of a cube is increasing at a constant rate. Prove that the increase in surface area varies inversely as the length of the edge of the cube.

Explanation

To prove that the increase in surface area of a cube varies inversely as the length of the edge of the cube when the volume is increasing at a constant rate, we can follow these steps:

### Step 1: Define the variables
Let the length of the edge of the cube be denoted as \( a \). The volume \( V \) of the cube can be expressed as:
\[ V = a^3 \]

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