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 step by step, we will use the relationship between the volume of a sphere and its radius, along with the concept of related rates in calculus.

### 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
...