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If V=(4)/(3)pir^(3), at what rate in cub...

If `V=(4)/(3)pir^(3)`, at what rate in cubic units is V increasing when r = 10 and `(dr)/(dt)` = 0.01?

A

`pi`

B

`4pi`

C

`40pi`

D

`4pi//3`

Text Solution

Verified by Experts

The correct Answer is:
B
We have,
`V=(4)/(3) pir^(3)`
`implies(dV)/(dt)=4pir^(2)(dr)/(dt)`
`implies (dV)/(dt)=4pixx100xx0.01 " "[because r = 10 and (dr)/(dt)=0.01]`
`implies (dV)/(dt)=4pi`
Hence, V is increasing at the rate of `4pi` cubic units per unit of time.
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