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5 June, 06:56

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 your answer to the nearest whole number. A. 85.4 m2 B. 74.6 m2 C. 8.54 m2 D. 746.67 m2

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  1. 5 June, 08:12
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    The answer is "85.4 m²".

    To find the area, first we have to find the radius; and given that height = 6mchord = 20 mNow, 20 m = 2 √ [ 6m (2 x radius - 6 m) ] 20 m / 2 = 2 √[ 6m (2 x radius - 6 m) ] / 2 10 m = √ [ 6m (2 x radius - 6 m) ] (10 m) ² = √[ 6m (2 x radius - 6 m) ] ² 100 m² = 6 m (2 x radius - 6 m) 100 m² = 12 m x radius - 36 sq m 100 m² + 36 m² = 12 m x radius - 36 m² + 36 m² 136 m² = 12 m x radius 136 m² / 12 m = 12 m x radius / 12 m 11.333 m = radius

    Thus radius is 11.333m.

    t. To find the area beneath an arc:

    Area = r² x arc cosine [ (r - h) / r ] - (r - h) x √ (2 x r x h - h²).

    r² = (11.333 m) ² = 128.444 m² r - h = 11.333 m - 6 m = 5.333 m r * h = 11.333 m x 6 m = 68 m²

    Area = 128.444 m² x arc cosine [ 5.333 m / 11.333 m ] - 5.333 m x √[ 2 x 68 m² - 36 m² ]

    Area = 128.444 m² x arc cosine [ 0.4706 ] - 5.333 m x √ [ 100m² ]

    Area = 128.444 m² x 1.0808 radians - 5.333 m x 10 m

    Area = 138.828 m² - 53.333 m²

    Area = 85.4 m²
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