Question

The radius of an air bubble is increasing at the rate of ½ cm/s. At what rate is the volume of the bubble increasing when the radius is 1 cm?

Answer 1

The air bubble is in the shape of a sphere. Now, the volume of an air bubble (V) with radius (r) is given by,

The rate of change of volume (V) with respect to time (t) is given by,

Hence, the rate at which the volume of the bubble increases is 2π cm³/s.