An edge of a variable cube is increasing at the rate of 10cm/sec. How fast the volume of the cube is increasing when the edge is 5cm long?

Explanation

To solve the problem step by step, we will use the relationship between the edge of the cube and its volume, and apply the concept of derivatives to find the rate at which the volume is increasing.

### Step-by-Step Solution:

**Step 1: Define the variables.**
Let \( x \) be the length of an edge of the cube in centimeters. The volume \( V \) of the cube is given by the formula:
\[
V = x^3
...