The radius of an air bubble is increasing at the rate of 12cms-1. Determine the rate of increase in it's volume when the radius is 1 cm.

Volume of the spherical bubble v=43πR3differentiating both sides w.r.t. time     dVdt=ddt43πR3⇒dVdt=43π3R2dRdt ⇒dVdt=4πR2dRdtat R=1 cm and when dRdt=12 cms-1, we have dVdt=4π×12×12 =2π cm3s-1 =6.28 cm3s-1