Question

Find the area of the minor segment of a circle of radius 14 cm, when its central angle is 60˚. Also find the area of the corresponding major segment.[use π=22/7]

Answer 1

Radius of the circle = 14 cm
Central Angle, 𝜽 = 60°,
Area of the minor segment

`=theta/360^@xxpir^2-1/2r^2sintheta`

`=60^@/360^@xxpixx14^2-1/2xx14^2xxsin60^@`

`=1/6xx22/7xx14xx14-1/2xx14xx14xxsqrt3/2`

`=(22xx14)/3-49sqrt3`

`=(22xx14)/3-(147sqrt3)/3`

`=(308-147sqrt3)/3 cm^2`

Area of the minor segment= `(308-147sqrt3)/3 cm^2`