The circumference of a circle is measured as 56 cm with an error 0.02 cm, The percentage error in its area, is

The circumference of a circle is measured as 56 cm with an error 0.02 cm, The percentage error in its area, is

  1. A

    17

  2. B

    128

  3. C

    114

  4. D

    156

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    Solution:

    Let r be the radius, C be the circumference and A

    be the area of the circle. Then,

    C=2πr and A=πr2

     ΔC=dCdrΔr and ΔA=dAdrΔr

     ΔC=2πΔr and ΔA=2πrΔr

    We have, C=56 and ΔC=0.02

     ΔCC=0.0256=12800 2πΔr2πr=12800Δrr=12800 ΔAA×100=2πrΔrπr2×100=2Δrr×100=2×128=114

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