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The volume of a sphere is increasing at a rate of $10 m^{3} s^{- 1} .$

Find a formula for the rate of increase of the surface area of the sphere, in terms of $r .$

We know that $\frac{d V}{d t} = 10.$

If you can find $\frac{d V}{d r}$ and $\frac{d A}{d r}$ then you can use

\frac{d A}{d t} = \frac{d A}{d r} \times \frac{d r}{d V} \times \frac{d V}{d t}

Recall that, for a sphere,

V = \frac{4}{3} π r^{3}

and

A = 4 π r^{2}

The answer is

\frac{k}{r}

Give the value of $k$