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

A sector is cut from a circle of radian $21cm.$

Area of circle = $\pi r^2$

Given $r=21cm.$

$\therefore$ Area = $\pi (21{)}^2$

$=441.\pi c{m}^2$

$\therefore$ Given angle of the sector = ${150}^{\circ }$

$\therefore$ fraction of circle = $\frac{150}{360}=\frac{5}{12}$

$\therefore$ Sector occupies the area of $\frac{5}{12}\times 441\pi$

$=\frac{5}{12}\times 441\times \frac{22}{7}$

$=577.5c{m}^2$

length of the arc = $\frac{5}{12}$ of circumference

$=\frac{5}{12}\times 2\pi r$

$=\frac{5}{12}\times 2\times \frac{22}{7}\times 21=55cm$