Gas is being pumped into a spherical balloon at the rate of 30ft3/min Then the rate at which the radius increases when is reaches the value 15 ft,  is

Gas is being pumped into a spherical balloon at the rate of 30ft3/min Then the rate at which the radius increases when is reaches the value 15 ft,  is

  1. A

    130πft/min

  2. B

    115πft/min

  3. C

    120ft/min

  4. D

    125ft/min

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    Solution:

    Let r be the radius of the spherical balloon and V 

    be the volume at any time t.

    It is given that  dVdt=30ft3/min

    Now, V=43πr3

     dVdt=4πr2drdt dVdtr=15=4π×152×drdtr=15 30=900πdrdtr=15 drdtr=15=130πft/min 

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