The rate of change of surface area of a sphere of radius r when the radius is increasing at the rate of 2 cm/ sec  is proportional to

The rate of change of surface area of a sphere of radius r when the radius is increasing at the rate of 2 cm/ sec  is proportional to

  1. A

    1r2

  2. B

    1r

  3. C

    r2

  4. D

    r

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    Solution:

    Let S be the surface area and r be the radius of the

    sphere at any time t. Then, 

               S=4πr2 dSdt=8πrdrdt dSdt=8πr×2                              drdt=2cm/sec

     dSdt=16πrdSdtr

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