The volume of a cube is increasing at the rate of `8 cm^3//s`. How fast is the surface area increasing when the length of an edge is 12 cm?

Explanation

To solve the problem of how fast the surface area of a cube is increasing when the length of an edge is 12 cm, given that the volume of the cube is increasing at a rate of \(8 \, \text{cm}^3/\text{s}\), we can follow these steps:

### Step 1: Understand the relationship between volume and edge length of the cube.
The volume \(V\) of a cube with edge length \(a\) is given by the formula:
\[ V = a^3 \]

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