Question

 A chord of a circle of radius 20 cm subtends an angle of 90° at the centre. Find the area of the corresponding major segment of the circle.

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Answer 1

r = 20cm 

theta = 90 degree

area of sector = theta/360 * pi * r2
= 90/360 * 22/7 * 20 * 20
= 1/4 * 22/7 * 20 * 20
= 2200/7
314.2 cm2

area of triangle = 1/2 * base * height

= 1/2 * 20 * 20 ( base and height both are r )

= 200 cm2

Area of minor segment = 314.2 - 200 = 114.2 cm2

major segment = area of circle - 114.2
= pi * r2 - 114.2
=22/7 * 20 * 20 -114.2 
= 1142 .94 cm2

Answer 2

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