2013 THREE(e)

A spherical balloon is being inflated with helium.

The balloon is being inflated in such a way that its volume is increasing at a constant rate of
$300{\text{ cm}}^3{\text{ s}}^{-1}$.

The material that the balloon is made of is of limited strength, and the balloon will burst when
its surface area reaches $7500{\text{ cm}}^2$.

Find the rate at which the surface area of the balloon is increasing when it reaches bursting
point.

*Show any derivatives that you need to find when solving this problem.*