If an error of 1 ° is made in measuring the angle of a sector of radius 30 cm, then the approximate error in its area, is

If an error of 1 ° is made in measuring the angle of a sector of radius 30 cm, then the approximate error in its area, is

  1. A

    450 cm2

  2. B

    25π cm2

  3. C

    2.5πcm2

  4. D

    none of these

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    Solution:

    Let A be the area and 0 (in radians) be the sector angle.  Then,

    A=12×302×θ=450θ=dAdθ=450                                 A=12r2θ

    Let Δθ be an error in θ and ΔA be the corresponding error in A.

    Then,
    ΔA=dAdθΔθ=ΔA=450×π180                           Δθ=1=π180 radians =ΔA=2.5πcm2

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