The circumference of a circle is measured as 28 cm with an error of 0.01 cm. The percentage error in the area, is

The circumference of a circle is measured as 28 cm with an error of 0.01 cm. The percentage error in the area, is

  1. A

    114

  2. B

    0.01

  3. C

    17

  4. D

    none of these

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    Solution:

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

    area of the circle. Then. C=2πr and A=πr2.

        A=πC2π2    A=c24π    dAdC=C2π

    ΔA=dAdCΔCΔA=C2πΔC ΔAA×100=c2π×cc24π×100=2ΔCC×100=2×0.0128×100=114

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