Solid mensuration

The area of a segment of a circle is 330 square meter. If the longest chord of the segment is 57 meter,find its radius.

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  1. recall that the area of a segment is

    a = 1/2 r^2 (θ-sinθ)

    If the longest chord is c, then

    (c/2)/r = sin(θ/2)

    So, now we have

    27.5 = r*sin(θ/2)
    330 = 1/2 r^2 (θ-sinθ)

    Solve those two and you have

    θ = 1.24
    so, r = 47.33

    as always, check my math

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    posted by Steve

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