Question

20.) Find the area of the minor segment of a circle of raduis 42cm, if length of the corresponding arc is 44cm.

Answer 1

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Answer 2

Find the circumference of the circle

Circumference = 2πr

                          = 2π(42)

                         = 264 cm

Find the fraction of the sector:

Given that the arc is 44 cm

The fraction of the segment = 44/264 = 1/6

Find the angle of the sector:

Angle = 1/6 x 360 = 60º

Find the area of the circle:

Area = πr²

        = π(42)²

        = 5544 cm²

Find the area of the sector:

Area of the segment = 1/6 x 5544

                                   = 924 cm²

Find the area of the triangle:

Area of the triangle = 1/2 AB sin C

                                 = 1/2 (42)(42) sin 60º

                                 = 441√3 cm²

Find the area of the segment:

Area of the segment = Area of the sector - Area of the triangle

                                  = 924 - 441√3

                                  = 160.17 cm²

Answer: 160.17 cm²