Question

A sector is cut from a circle of radius 21 cm. The angle of the sector is ${150}^{\circ }$. Find the length of the arc and the area of the sector.

Answer 1

Length of the arc $=2\pi r\times \frac{\theta }{{360}^o}=2\times \frac{22}{7}\times 21\times \frac{{150}^o}{{360}^o}=55cm$

Area of the sector $=\pi r^2\times \frac{\theta }{{360}^o}=\frac{22}{7}\times 21\times 21\times \frac{{150}^o}{{360}^o}=577.5c{m}^2$