Question

Find the area of the minor segment of a circle of radius 14 cm, when its central angle is ${60}^o$. Also find the area of the corresponding major segment. $[Use\pi =\frac{22}{7}]$

Answer 1

Given the radius of a circle is $14$ cm and a minor segment of the central angle is also ${60}^{\circ }$.

We know that area of segment =$\pi r^2\left(\frac{c}{360}\right)$ (where c is the central angle of segment and r is a radius of the circle)

Then area of minor segment =$\frac{22}{7}\times (14{)}^2\times \frac{60}{360}=\frac{22\times 2\times 14}{6}=102.67c{m}^2$

We know that the total area of circle =$\pi r^2=\frac{22}{7}(14{)}^2=22\times 2\times 14=616c{m}^2$

Then area of major arc =$616-102.67=513.33c{m}^2$