If the rate of change of volume of a sphere is equal to the rate of change of its radius, then its radius is equal to

If the rate of change of volume of a sphere is equal to the rate of change of its radius, then its radius is equal to

  1. A

    1 unit 

  2. B

    2π units 

  3. C

    12π unit 

  4. D

    12π unit 

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    Solution:

    Let r be the radius and V be the volume of the

    sphere. Then,

                V=43πr3 dVdt=4πr2drdt

     drdt=4πr2drdt                         dVdt=drdt (given) 

     4πr2=1r=12π

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