Question

A chord of a circle of radius 30 cm makes an angle of 60° at the centre of the circle. Find the areas of the minor major segments. [take pi = 3.14 and √3 = 1.73]

Answer 1

Radius of circle = r = 30 cm

Area of minor segment = Area of sector – Area of triangle …(1)

Area of major segment = Area of circle – Area of minor segment …(2)

Area of sector = θ/360 x πr²

= 60/360 x 3.14 x 30 x 30

= 471 cm²

Area of triangle = √3/4 (side)² (Since it form a equilateral triangle)

= √3/4 x 30 x 30

= 389.7 cm²

(1) ⇨

Area of minor segment = 471 – 389.7 = 81.3 cm²

(2) ⇨

Area of major segment = π(30²) – 81.3 = 2744.7 cm²

Answer:

Area of major segment is 2744.7 cm² and of minor segment is 81.3 cm².