A stone is dropped into a quiet lake. If the waves moves in circles at the rate of 30 cm/sec when the radius is 50 m, the rate of increase of enclosed area, is 

A stone is dropped into a quiet lake. If the waves moves in circles at the rate of 30 cm/sec when the radius is 50 m, the rate of increase of enclosed area, is 

  1. A

    30πm2/sec

  2. B

    30m2/sec

  3. C

    3πm2/sec

  4. D

    none of these 

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    Solution:

    Let the radius of the circular wave ring be r cm at any time t.

     Then drdt=30cm/sec (Given)

    Let A be the area of the enclosed ring. Then, 

    A=πr2 dAdt=2πrdrdt dAdt=2π×50×30100m2/sec=30πm2/sec

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