Question

The radius of a circle with centre O is $7\text{cm}$ . Two radii OA and OB are drawn at right angles to each other. Find the areas of minor and major segments.

Answer 1

Radius of a circle $=7\text{cm}$

Area of circle $=\pi r^2=\frac{22}{7}\times 7\times 7=154{\text{cm}}^2$
Area of minor segment $=$ Area of minor sector $-$ area of triangle

$=\frac{\pi r^2\times \theta }{360}-\frac{1}{2}{r}^2\sin \theta$ $[\because \theta$ is the angle subtended by the minor segment at the centre $]$

$=\frac{22}{7}\times 7\times 7\times \frac{90}{360}-\frac{1}{2}\times 7\times 7\times \sin {90}^{\circ }$ $[\because \theta ={90}^{\circ }]$

$=\frac{77}{2}-\frac{49}{2}=\frac{77-49}{2}=\frac{28}{2}=14{\text{cm}}^2$

Area of major segment $=$ Area of circle $-$ Area of minor segment
$=154-14=140{\text{cm}}^2$
Therefore, area of major segemnt is $140{\text{cm}}^2$

'