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Question

The radius of a cylinder is increasing at a rate of 3 msec and its altitude is decreasing at a rate of 4msec.

The rate of change of volume when radius is 4m and altitude is 6m is


A

80πm3sec

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B

144πm3sec

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C

80m3sec

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D

60m3sec

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Solution

The correct option is A

80πm3sec


Explanation for the correct option:

Given that,

  • The radius of a cylinder is increasing at a rate of 3 msec drdt= 3 msec
  • Altitude is decreasing at a rate of 4msecdhdt=-4msec
  • Radius is r=4m and altitude is h=6m

We know that Volume of cylinder is given by V=πr2h

Differentiating both sides with respect to t,

dVdt=ddtπr2h=πhddtr2+r2dhdtddxU·V=VdUdx+UdVdxdVdt=π2rhdrdt+r2dhdtddtxn=nxn-1dxdtdVdtr=4,h=6=π2463+42-4drdt=3,dhdt=-4=π144-64dVdtr=4,h=6=80πm3sec

Hence, the correct option is option (A) i.e. 80πm3sec


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