The radius of a spherical soap bubble is increasing at the rate of 0.2 cm/sec. Find the rate of increase of its surface area, when the radius is 7 cm.

Explanation

To solve the problem, we need to find the rate of increase of the surface area of a spherical soap bubble when its radius is 7 cm, given that the radius is increasing at a rate of 0.2 cm/sec.

### Step-by-Step Solution:

1. **Identify the given information:**
- The rate of change of the radius, \( \frac{dr}{dt} = 0.2 \) cm/sec.
- The radius at which we need to find the rate of increase of the surface area, \( r = 7 \) cm.

...