Question

Find the area of the segment of a circle of radius 7 cm whose corresponding sector has a central angle of 60° (π = 3.14).

Answer 1

Given:

Radius r = 7 cm

Central angle θ = 60°

Use π = 3.14

Area of sector = `θ/360 xx pir^2`

= `60/360 xx 3.14 xx 7 xx 7`

= `1/6 xx 153.86`

≈ 25.64 cm²

Area of triangle = `1/2 r^2 sin θ`

= `1/2 xx 7 xx 7 xx sin 60°`

= `49/2 xx sqrt3/2`

= `(49 xx 1.732)/4`

= `(84.868/4)`

≈ 21.22 cm²

Area of segment = Area of sector − Area of triangle

= 25.64 − 21.22

= 4.42 cm²