Area of circular sectors?

"Prove that the area of a circular sector of radius r with central angle Ø is A=(1/2)Ør^2, where Ø is measured" Could anyone help me with it? Not just the answer, but step by step?

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  • 1 decade ago
    Favorite Answer

    A_sector = A_circle (θ/(2π)) ....... geometrically

    = πr² (θ/(2π))

    = 1/2 r²θ

    A = ∫ ∫ r dr dθ ........ calculus

    = 1/2r² ∫ dθ

    = 1/2r²θ

    Answer: see above

  • ciel
    Lv 4
    4 years ago

    a million. There are 2 pi radians in an entire circle. the area of a circle of radius 10m is A = pi r^2 = pi (10m)^2 = one hundred pi m^2. the area of a sector with suitable perspective a million radian is (one hundred pi m^2) * (a million / (2 pi)) = 50 m^2 answer: 50 m^2 2. sixteen m^2 = (pi r^2) * (2 / (2 pi)) = pi r^2 * (a million / pi) = r^2 r^2 = sixteen m^2 r = 4m answer: The radius is 4 meters.

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