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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:

4/9

None of these

6/7

2/9

Solution:

The volume of spherical balloon is given by
V = (4/3)πR³
Initial volume = 4500π
After 49 minutes volume = 4500π − (72π)(49) = 972π
By solving these above equations, we get
r = 9 (Radius of the balloon 49 minutes after the leakage)