Gas is being pumped into a a spherical balloon at the rate of `30 ft^(3)//min`. Then the rate at which the radius increases when it reaches the value 15 ft, isA. `(1)/(30pi) ft//min`B. `(1)/(15pi)ft//min`C. `(1)/(20)ft//min`D. `(1)/(25)ft//min`

Gas is being pumped into a a spherical balloon at the rate of `30 ft^(

1.	Gas is being pumped into a a spherical balloon at the rate of `30 ft^(3)//min`. Then the rate at which the radius increases when it reaches the value 15 ft, isA. `(1)/(30pi) ft//min`B. `(1)/(15pi)ft//min`C. `(1)/(20)ft//min`D. `(1)/(25)ft//min`
Answer» Correct Answer - A Let r be the radius of the spherical balloon and V be the volume at any time t. It given that `(dV)/(dt) = 30 ft^(3)//min` Now, `V=(4)/(3) pi r^(3)` `implies (dV)/(dt)=4 pi r^(2)=(dr)/(dt)` `implies ((dV)/(dt))_(r=15) = 4pi xx 15^(2)xx((dr)/(dt))_(r=15)` `implies 30 = 900pi ((dr)/(dt))_(r=15)` `implies ((dr)/(dt))_(r=15)=(1)/(30pi) ft//min`

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Gas is being pumped into a a spherical balloon at the rate of `30 ft^(3)//min`. Then the rate at which the radius increases when it reaches the value 15 ft, isA. `(1)/(30pi) ft//min`B. `(1)/(15pi)ft//min`C. `(1)/(20)ft//min`D. `(1)/(25)ft//min`

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