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

Explanation

Let r be the radius and V be the volume of the balloon.
`:. V= 4/3 pi r^(3)`
`rArr (dV)/(dr) = 4 pi r^(2)`
at r 10 cm
` (dV)/(dr) = 4 pi (10)^(2) = 400 pi`
` :. ` Volume of balloon is changing at the rate of ` 400 pi cm^(3)`/sec.