Question

a chord AB of a circle of radius 10cm makes a right angle at the centre of circle. Find area of major segment of the circle.

Answer 1

Area of circle = pi × r × r

= 3.14 × 10 × 10

= 3.14 × 100

= 314 cm square

Area of minor segment = { pi × 90 ÷ 360 - sin 45 cos 45 } × r × r

= { 3.14 × 1÷4 - 1÷√2 ×1 ÷ √2 } × 10×10

= { 3.14 ×1÷4 - 1÷ 2 } × 100

={ 3.14 × 100÷4 - 100 ÷2 }

= 314÷4 - 50

= 78.5 - 50

= 28.5

Area of major segment = area of circle - area of minor segment

= 314 - 28.5

= 285.5 cm

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