Question

The radius of a sector is 42 cm and its sector angle is ${60}^o$. Find its are length, area and perimeter.

Answer 1

Given that radius r=42 cm and $\theta ={60}^{\circ }$.

Therefore,

length of arc $l=\frac{\theta }{{360}^{\circ }}\times 2\pi rl=\frac{\theta }{{360}^{\circ }}\times 2\pi r$

$=\frac{{60}^{\circ }}{{360}^{\circ }}\times 2\times \frac{22}{7}\times 42=44cm.=\frac{{60}^{\circ }}{{360}^{\circ }}\times 2\times \frac{22}{7}\times 42=44cm.$

Area of the sector $=\frac{lr}{2}=\frac{44\times 42}{2}=924c{m}^2$

$Perimeter=l+2r=44+2\left(42\right)=128cm$