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A spherical balloon is expanding. If the...

A spherical balloon is expanding. If the radius in increasing at the rate of 2 inches per minute the rate at which the volume increases (in cubic inches per minute) when the radius is 5 inches is

A

`10 pi`

B

`100 pi`

C

`200 pi`

D

`50 pi`

Text Solution

Verified by Experts

The correct Answer is:
C
The volume `V=4/3pir^(3), r` being the radius given that `(dr)/(dt)=2` inch/min
`(dV)/(dt)=4pir^(2) (dr)/(dt)`
`implies (dV)/(dt):|_(r=5)=4pi(25)(2)=200pi`
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