Question

Find the area of minor segment of a circle of radius 14 cm, when the angle of the corresponding sector is 60⁰ .

Answer 1

Area of the minor segment of the circle = $\frac{\theta }{360}\times {\mathrm{\pi r}}^2-{\mathrm{r}}^2\sin \frac{\mathrm{\theta }}{2}\cos \frac{{\displaystyle \mathrm{\theta }}}{{\displaystyle 2}}$
$$\begin{gathered} =\frac{60}{360}\times \mathrm{\pi }{\left(14\right)}^2-{\left(14\right)}^2\sin \frac{60}{2}\cos \frac{60}{2} \\ ={\left(14\right)}^2\left[\frac{1}{6}\mathrm{\pi }-\frac{1}{2}\times \frac{\sqrt{3}}{2}\right] \\ =\left(\frac{308}{3}-49\sqrt{3}\right){\mathrm{cm}}^2 \end{gathered}$$