Answer
$\dfrac{dV}{dt}=4\pi r^2\dfrac{dr}{dt}$
Work Step by Step
Differentiate $V=\dfrac{4}{3}\pi r^3$ with respect to $t$.
We get, $\dfrac{dV}{dt}=\dfrac{4}{3}\pi \times3r^2\dfrac{dr}{dt}$
Now simplify.
We get, $\dfrac{dV}{dt}=4\pi r^2\dfrac{dr}{dt}$
Which is the required relation.
