Find the area of the shaded segment of the circle

Mathematics

1 answer:

hoa [83]3 years ago

6 0

Answer:

15.35 m²

Step-by-step explanation:

For a central angle of θ in radians, the area of a segment is ...

A = (1/2)r²(θ -sin(θ))

The central angle subtending the segment is 120°, or 2π/3 radians. Thus the segment area is ...

A = (1/2)(5 m)²(2π/3 -sin(2π/3)) = (25 m²)(π/3 -(√3)/4)

A ≈ 15.35 m² . . . . area of shaded segment

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