Given as the radius of an air bubble is increasing at the rate of 0.5 cm/sec
As to find the rate at which the volume of the bubble increasing when the radius is 1 cm
Suppose the radius of the given air bubble be r cm and let V be the volume of the air bubble at any instant time
Now, according to the given question,
The rate of increasing in the radius of the air bubble is, dr/dt = 0.5 cm/sec ...(i)
As we know that the volume of the bubble is V = (4/3)πr3
By applying derivative with respect to time on both sides
...(ii)
Therefore, when the radius is 1cm, so the above eqn. becomes
Thus the rate at which the volume of the air bubble is increasing when the radius is 1 cm.
