The radius of an air bubble is increasing at the rate of 0.5 cm/sec. At what rate is the volume of the bubble increasing when the radius is 1 cm?

Explanation

Let r be the radius and V be the volume of the air bubble.
Given ` (dr)/(dt) = 1/2 ` cm/sec
Now, ` V= 4/3 pi r^(3)" "rArr (dV)/(dt) = 4 pi r^(2) (dr)/(dt)`
at r = 1 cm
` (dV)/(dt) = 4 pi (1)^(2)* 1/2 = 2pi cm^(3)//sec`
Therefore, the volume of bubble is increasing at the rate of ` 2pi cm^(3) //sec`