Question

A sector is cut from a circle of radius 21 cm. The angle of the sector is 150°. Find the length of the arc and the area of the sector.

Answer 1

Given:
Radius = 2 cm
Angle of sector = ${150}^{\circ }$
Now,
$$\begin{gathered} \mathrm{Length}\mathrm{of}\mathrm{the}\mathrm{arc}=\frac{2\mathrm{\pi r}\theta }{360} \\ =\frac{2\times {\displaystyle \frac{22}{7}}\times 21\times 150}{360} \\ =55\mathrm{cm} \end{gathered}$$

Area of the sector =$\frac{{\mathrm{\pi r}}^2\theta }{360}$

$$\begin{gathered} =\frac{22}{7}\times 21\times 21\times \frac{150}{360} \\ =577.5\mathrm{cm} \end{gathered}$$