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Question

The radius of a cylinder is increasing at the rate of 3m/s and its altitude is decreasing at the rate of 4m/s. The rate of change of volume, when radius is 4mand altitude is 6m, is


A

80πcum/s

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B

144πcum/s

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C

80cum/s

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D

64cum/s

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Solution

The correct option is A

80πcum/s


Explanation for the correct option

Let the radius of the of the cylinder is r and h the altitude/ height of the cylinder

Given, rate of increase of radius is 3m/s

That is drdt=3m/s

The rate of decrease of altitude is 4m/s

That is dhdt=-4m/s

We know that volume of the cylinder is V=πr2h

On differentiating the volume with respect to t

dVdt=πr2dhdt+2πrhdrdt

At r=4mand h=6m,

dVdt=π42-4+2π463=-64π+144π=80πm3/s

Hence option A is correct


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