Question

A spherical balloon is filled with 4500π cubic meters of helium gas. If a leak in the balloon causes the gas to escape at the rate of 72π cubic meters per minute, then the rate (in meters per minute) at which the radius of the balloon decreases 49 minutes after the leakage began is

(A) 9/7

(B) 7/9

(C) 2/9

(D) 9/2

Answer 1

Answer is (C) 2/9

Volume of the sphere is given by: v = 4/3πr³

After 49 minutes of leakage, the volume is: 4500π − 49(72π) = 972π.

Therefore,

Therefore, the rate (in meters per minute) at which the radius of the balloon decreases 49 min after the leakage began is