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.

Answer 1

Area of a quadrant sector of the circle = (90/360) * (pi* 20*20)

=> 100 pi sq cm

Area of corresponding right triangle

= 1/2 * 20 * 20 = 200 sq cm

=> Area of minor segment = (100pi - 200) sq cm

=> Area of major segment =

Pi r^2 - ar( minor segment )

= 400 pi - (100 pi - 200)

=(300pi + 200) sq cm 

OR

300*3.14 + 200

= 942 + 200 = 1142 sq cm (approx)