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Math Help - eplain please? find the area of a Circular sigment

  1. #1
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    eplain please? find the area of a Circular sigment

    Problem 1

    What is the area of the shaded portion of the circular segment shown in the
    figure below, given a = 50 deg and r = 2 ?

    Problem 1


    Approach:
    Look up mensuration formula for a circular segment.


    Given:
    a = 50 deg
    r = 2


    By Definition:
    Area for circular segment
    A =
    r2(a - sina)/2


    Solve:
    A = r2(a - sina)/2
    a = 50 deg = 50 deg 2
    p rad / 360 deg
    a =
    0.27778 p rad
    r = 2
    Substitute:
    A =
    22( 0.27778 p - sin 50)/2
    A =
    0.213

    Why did they change 0.2777 and not leave it in degrees
    Answer is b) 0.213




    a) 0.425
    b) 0.213
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  2. #2
    MHF Contributor
    skeeter's Avatar
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    North Texas
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    Re: eplain please? find the area of a Circular sigment

    the formula for the area of a circular segment is based on a central angle measured in radians, not in degrees.

    area of a circular segment = sector area - triangle area

    A = \frac{\theta}{2\pi} \cdot \pi r^2 - \frac{1}{2} r^2 \sin{\theta}

    A = \frac{r^2}{2} \left(\theta - \sin{\theta}\right)
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