The volume of a cube is increasing at the rate of 9cm3/sec. How fast is the surface are increasing when the length of an edge is 10 cm?

Explanation

To solve the problem step by step, we will use the relationships between the volume and surface area of a cube, along with the rates of change.

### Step 1: Understand the given information
We know that the volume \( V \) of a cube is increasing at a rate of \( \frac{dV}{dt} = 9 \, \text{cm}^3/\text{sec} \). We also know that the length of an edge of the cube \( a = 10 \, \text{cm} \).

### Step 2: Write the formula for the volume of a cube
The volume \( V \) of a cube is given by:
\[
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