Imagine a balloon being filled with air. As time increases, the radius will increase, and the volume will increase.

We can see that the volume depends on time, and the radius depends on the volume - so what is the relationship between the radius and time?

This type of question brings us to study related rates of change.

A balloon is being inflated at a rate of $120{\text{cm}}^3{s}^{-1}.$ The balloon is modeled as a sphere of radius $r.$

When the radius is $16\text{cm}$ the balloon will pop.

What is the rate of increase of the radius of the balloon when it is half full?