A circular metal plate is heated so that its radius increases at a rate of 0.1 mm per minute. Then the rate at which the plate’s area is increasing when the radius is 50 cm, is 

A circular metal plate is heated so that its radius increases at a rate of 0.1 mm per minute. Then the rate at which the plate's area is increasing when the radius is 50 cm, is 

  1. A

    10π  mm/minute  

  2. B

    100π mm/minute 

  3. C

    π  mm/minute 

  4. D

    -π  mm/minute 

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    Solution:

    Let at any moment 't' the radius of the plate be and its area be A. Then,

    A=πr2dAdt=2πrdrdt

    when r=50cm=500mm,drdt=0.1=110 

    dAdt=2π×500×110=100πmm/ minute 

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