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Question

If V=43πr3,at what rate in cubic units is V increasing when r = 10 and drdt=0.01 ?


A

π

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B

4π

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C

40π

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D

4π3

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Solution

The correct option is B

4π


We have,
V=43πr3dvdt=4πr2drdtdvdt=4π×100×0.01[r=10 anddrdt=0.01]dvdt=rπ
Hence, V is increasing at the rate of 4π cubic units per unit of time.

Hence (b) is the correct answer.


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