1.33: Past-paper question 4

The surface area of a sphere with radius $\displaystyle r$ cm is increasing at a constant rate of $\displaystyle 50\pi$$\displaystyle \mathrm{cm}^{2}$/s

Find, in $\displaystyle \mathrm{cm}^{3}$, the exact volume of the sphere at the instant when the rate of increase

of $\displaystyle r$ is $\displaystyle \frac{5}{12}$ cm/s