A cylindrical vessel of radius 0.5 m is filled with oil at the rate of 0.25πm3/ minute. The rate at which the  surface of the oil is rising, is 

A cylindrical vessel of radius 0.5 m is filled with oil at the rate of 0.25πm3/ minute. The rate at which the  surface of the oil is rising, is

 

  1. A

    1 m/ minute

  2. B

    2 m/ minute

  3. C

    5 m/ minute 

  4. D

    1.25 m/ minute

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    Solution:

    Let r be the radius, h be the height and V be the

    volume of the oil at time t , Then,

              V=πr2h        V=π4h                                      r=0.5m=12( given )        

     dVdt=π4dhdt 0.25π=π4×dhdt                                dVdt=0.25πm3 (given) 

     dhdt=1m/ minute 

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