A balloon, which always remains spherical has a variable radius. Find the rate at which its volume is increasing with the radius when the later is 10 cm.

Let us assume that at any instant of time, the radius of the balloon be $r$ and its volume be $V$, then
$V = \cfrac{4}{3}\pi {r^3}$ …(i)

Differentiating (i) w.r.t. $r$, we get
$\cfrac{{dV}}{{dt}} = \left( {\cfrac{4}{3}\pi } \right)3{r^2} = 4\pi {r^2} = 4\pi {\left( {10{\rm{cm}}} \right)^2} = 400\pi {\rm{c}}{{\rm{m}}^3}$

Rate of increase of volume with respect to change in radius $= 400\pi {\rm{c}}{{\rm{m}}^{\rm{3}}}{\rm{/cm}}$