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 min after the leakage began is

TestHub · Accepted Answer

V = 3 4 ​ π r 3 ⇒ 4500 π = 3 4 π r 3 ​ ⇒ r = 15 m After 49 min = ( 4500 − 49.72 ) π = 972 π m 3 ⇒ ⇒ ​ ​ 972 π r 3 ​ = 3 4 ​ π r 3 = 3 × 243 = 3 × 3 5 ​ r d t d v ​ 72 π d t d r ​ ​ = 9 = 4 π r 2 ( d t d r ​ ) = 4 π × 9 × 9 ( d t d r ​ ) = ( 9 2 ​ ) ​

Mathematics - Application of Derivative Question with Solution | TestHub

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