A spherical balloon is filled with 4500 π cubic meters of helium gas. If a leak in the balloon causes the gas to escape at the rate of 72 π cubic meters per minute, then the rate (in meters per minute

Question

A spherical balloon is filled with 4500 π cubic meters of helium gas. If a leak in the balloon causes the gas to escape at the rate of 72 π 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

TestHub · Accepted Answer

v = 3 4 ​ π r 2 After 49 minutes volume = 4500 π − 49 ( 72 π ) = 972 π 3 4 ​ π r 3 = 972 π ⇒ r 3 = 729 ⇒ r = 9 v = 3 4 ​ π r 3 d t d v ​ = 3 4 ​ π 3 r 2 d t d r ​ 72 π = 4 π r 2 d t d r ​ dt dr ​ = 4 ⋅ 9 ⋅ 9 72 ​ = 9 2 ​

Mathematics - Application of Derivative Question with Solution | TestHub

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