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solid mensuration

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Determine the area of the segment of a circle if the length of the chord is 15 inches & located 5 inches from the center of the circle.

  • solid mensuration - ,

    Make your sketch
    let the radius be r
    r^2 = 5^2 + 7.5^2 = 81.25
    r - √81.25

    central angle formed by the chord:
    let Ø be the angle at the centre formed by the right-angled triangle

    tanØ = 5/7.5
    Ø = 33.69°
    central angle is 2Ø = 67.38°

    area of whole circle = π(√81.25)^2 = 81.25π

    so by simple ratio:
    area of sector:
    sector/84=1.25π = 67.38/360
    sector = ....

    area of triangle formed by the chord in that sector
    = (1/2)(15)(5) = 75/2

    area of segment = 75/2 - area of sector

    I will leave the button pushing up to you

  • solid mensuration - ,

    42.35

  • solid mensuration - ,

    89

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