A balloon, which always remains spherical on inflation, is being inflated by pumping in 900 cubic centimetres of gas per second. Find the rate at which the radius of the balloon increases when the radius is 15 cm.

Explanation

To solve the problem, we need to find the rate at which the radius of a spherical balloon increases when the radius is 15 cm, given that the volume of the balloon is increasing at a rate of 900 cubic centimeters per second.

### Step-by-Step Solution:

1. **Understand the Volume of a Sphere**:
The volume \( V \) of a sphere is given by the formula:
\[
V = \frac{4}{3} \pi r^3
...