Find the rate at which the volume of a spherical balloon will increase when its radius is 2 meters if the rate of increase of its redius is 0.3 m/min.

Explanation

Let r be the radius of a spherical ballon.
Give that dr/dt = 0.3 m/min.
If V be the volume of the ballon then `dV/dt = 3/4 pi r _3`.
`rArr Dv/dt = 3/4 pi cdot 3r^2 dr/dt = 4 pi r^2 dr/dt`
`therefore Dv/dt](r=2) = 4pi xx 4 xx cdot 3 = 4 cdot 8 pi m^3/min`
`therefore` The volume increase at the rate of `4 cdot 8 pi m^3/min`.