A balloon, which always remains spherical on inflation, is being inflated by pumping in 900 cubic centimetres of gas per second. Find the rate at which the radius of the balloon increases when the radius is 15 cm.

Explanation

Let 'r' be the radius and 'V' be the volume of the balloon.
Given, ` (dV)/(dt) = 900 cm^(3)//sec`
`V = 4/3 pi r^(3)`
`rArr (dV)/(dt) = 4 pi r^(2) (dr)/(dt)`
at r = 15 cm
`900 = 4 pi (15)^(2) (dr)/(dt)`
`rArr (dr)/(dt) = 1/pi = 7/22` cm/sec
Therefore, rate of increase in radius = `7/22` cm/sec