Question

Find the area of a segment of a circle with a central angle of 120 degrees and a radius of 8 cm. Express answer to the nearest integer.​

Answer 1

Area of segment, i.e. area of shaded region = area of sector OAPB− arΔABO

Area of sector OAPB =

360

0

θ

×πr

2

=

360

0

120

0

×

7

22

×4×4

=

21

352

cm

2

=16.76cm

2

Now, area of ΔOAB.

Draw OM1AB. This will results in forming OAB triangle in two 30

0

−60

0

−90

0

triangles.

Using arΔOAB=2×arΔOAM=2×

2

1

×OM×AM=2×2

3

=4

3

=4× 1.73=6.92cm

2

∴ area of segment =16.76−6.92=9.84≈10cm

2

Answer 2

THE CORRECT ANSWER IS 10CM.