Question

Find the area of the shaded segment of the circle​

Answer 1

≈ 0.8 m²

Explanation:

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FORMULA FOR FINDING AREA OF SEGMENT :-

`A = r^(2) [(\alpha )/(360) * \pi - (\sin (\alpha )/(2) * \cos (\alpha )/(2) )]`

Where :-

• A = Area of the segment
• r = Radius of the circle
• α (alpha) = Angle subtended by arc at the center

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Angle subtended by the minor arc at the center = 360° - 300° = 60°

Radius of the circle = 3 m

Area of the segment =

`3^(2) [ (60)/(360) * \pi - (\sin (60)/(2) * \cos (60)/(2))]`

`= 9[(1)/(6) * \pi - (\sin 30 * \cos 30)]`

`= 9[(\pi )/(6) - ((1)/(2) * (√(3) )/(2) )]`

`= 9[(\pi )/(6) - (√(3) )/(4) ]`

`= 9[(2\pi - 3√(3) )/(12) ]`

`= (9)/(12) * (2\pi - 3√(3))`

( Assuming √3 = 1.73 & π = 3.14 )

`= (3)/(4) * (6.28 - 5.19)`

`= 0.75 * 1.09`

`= 0.8175`

∴ Area of the segment ≈ 0.8 m² (rounding to the nearest tenth)