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Math Help - Segment of a Circle

  1. #1
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    Segment of a Circle

    What is the approximate area of a segment of a circle with a height 6 m and the length of the chord is 20 m? Round answer to the nearest whole number.
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  2. #2
    Member TheMasterMind's Avatar
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    Quote Originally Posted by magentarita View Post
    What is the approximate area of a segment of a circle with a height 6 m and the length of the chord is 20 m? Round answer to the nearest whole number.
    chord = 2 sqrt [ height x ( 2 x radius - height) ]

    Given the values 20 and 6;

    20 m = 2 sqrt 6 m x ( 2 x radius - 6 m )
    20 m / 2 = 2 sqrt 6 m x ( 2 x radius - 6 m ) / 2
    10 m = sqrt [ 6 m x ( 2 x radius - 6 m ) ]
    10 m squared = sqrt 6 m x ( 2 x radius - 6 m ) squared
    100 sq m = 6 m x ( 2 x radius - 6 m )
    100 sq m = 12 m x radius - 36 sq m
    100 sq m + 36 sq m = 12 m x radius - 36 sq m + 36 sq m
    136 sq m = 12 m x radius
    136 sq m / 12 m = 12 m x radius / 12 m
    11.333 m = radius

    A = r squared x arc cosine ( ( r - h ) / r ] - ( r - h ) x sqrt ( 2 x r x h - h squared )

    A = 128.444 sq m x arc cosine ( 5.333 m / 11.333 m ) - 5.333 m x sqrt ( 2 x 68 sq m - 36 sq m )

    A= 128.444 sq m x 1.0808 radians - 5.333 m x 10 m

    A= 85.4 sq m= 85 sq m
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  3. #3
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    ok...

    Quote Originally Posted by TheMasterMind View Post
    chord = 2 sqrt [ height x ( 2 x radius - height) ]

    Given the values 20 and 6;

    20 m = 2 sqrt 6 m x ( 2 x radius - 6 m )
    20 m / 2 = 2 sqrt 6 m x ( 2 x radius - 6 m ) / 2
    10 m = sqrt [ 6 m x ( 2 x radius - 6 m ) ]
    10 m squared = sqrt 6 m x ( 2 x radius - 6 m ) squared
    100 sq m = 6 m x ( 2 x radius - 6 m )
    100 sq m = 12 m x radius - 36 sq m
    100 sq m + 36 sq m = 12 m x radius - 36 sq m + 36 sq m
    136 sq m = 12 m x radius
    136 sq m / 12 m = 12 m x radius / 12 m
    11.333 m = radius

    A = r squared x arc cosine ( ( r - h ) / r ] - ( r - h ) x sqrt ( 2 x r x h - h squared )

    A = 128.444 sq m x arc cosine ( 5.333 m / 11.333 m ) - 5.333 m x sqrt ( 2 x 68 sq m - 36 sq m )

    A= 128.444 sq m x 1.0808 radians - 5.333 m x 10 m

    A= 85.4 sq m= 85 sq m
    Wonderfully done!
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