2019 ONE(e)

The volume of a sphere is increasing.

At the instant when the sphere’s radius is $0.5$ m, the surface area of the sphere is increasing at
a rate of $0.4$ m${}^2$ s${}^{-1}$.

Find the rate at which the volume of the sphere is increasing at this instant.

*You must use calculus and show any derivatives that you need to find when solving this
problem.*