The volume of a spherical balloon is increasing at the rate of 20 cm^3/sec . Find the rate of change of its surface area at the instant when radius is 5 cm.

Explanation

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

### Step 1: Understand the given information
We are given that the volume \( V \) of a spherical balloon is increasing at the rate of \( \frac{dV}{dt} = 20 \, \text{cm}^3/\text{sec} \). The radius \( r \) of the balloon at the moment we are interested in is \( r = 5 \, \text{cm} \).

### Step 2: Write the formulas for volume and surface area
The volume \( V \) of a sphere is given by:
\[
...