Solid Mensuration

A circle having an area of 452 square inches is cut into two segments by a chord, which is 6 inches from the center of the circle. Find the area of the bigger segment.

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  1. the radius of the circle is 12. So, the angle θ subtended by the chord is 2π/3.

    The area of the smaller segment is

    1/2 r^2 (θ-sinθ)

    That should get you started.

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  2. A of smaller segment = .5r^2((theta in rad) - sin (theta in degrees))

    theta = 2(arccos(6/12))
    theta=120

    A of larger segment = A of circle - A of smaller segment
    A = 452 - 12^2((120pi/180) - sin120)/2
    A = 363.557

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