Question

What's 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. 746.67 m2

Answer 1

Hello!

The Correct Answer to this would be 100%:

Option "85.4".

(Work Below)

Given:
height = 6m
chord = 20 m

We need to find the radius of the circle.

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

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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