Question

Find the area of both the segments of a Circle of radius $43cm$ with central angle ${120}^{\circ }.$ [Given, $\sin {120}^{\circ }=\frac{\sqrt{3}}{2}and\sqrt{3}=1.73$]

Answer 1

Given the angle of the circle in ${120}^o$

Minor segment cover ${120}^o$

Major segment cover $360-120={240}^o$

$\therefore$ Area of circle $=\pi r^2$

Given $r=43cm$

$\therefore$ Area of circle $=(43{)}^2\pi$

$=1849\pi$

$\therefore$ fraction of circle with angle ${120}^o$

$=\frac{{120}^o}{360}=\frac{1}{3}$

$\therefore$ Area of segment $=\frac{1}{3}\times 1849\pi$

$=616.33\pi$

$\therefore$ fraction of circle with angle ${240}^o$

$=\frac{240}{360}=\frac{2}{3}$

$\therefore$ Area of segment $=\frac{2}{3}\times 1849\pi$

$=1232.67\pi$