Question

A chord of a circle of radius $12cm$ stands an angle of ${120}^{\circ }$ at the centre. Find the area of the corresponding segment of the circle.

Answer 1

Given : Radius of circle = 12 c

$\theta ={120}^{\circ }$

Area of the segment =

$\{\frac{\pi }{360}\times \theta -sin(\frac{\theta }{2}\left)cos\right(\frac{\theta }{2}\left)\right\}{r}^2$

$=\{\pi \times \frac{1}{3}-sin{60}^{\circ }cos{60}^{\circ }\}12\times 12$

$=(\frac{\pi }{3}-\frac{\sqrt{3}}{2}\times \frac{1}{2})144$

$=(\frac{3.14}{3}-\frac{1.732}{4})\times 144$

$=\frac{12.56-5.196}{12}\times 144$

$=7.364\times 12=88.368c{m}^2$