Question

In a circle of radius $21$ cm, an arc subtends an angle of ${60}^o$ at the center, then find the length of the arc.

Answer 1

Relation between angle subtended by chorel on minar & major arc

minar arc = angle subtended less than ${180}^o$

minar arc = angle subtended less mor ${180}^o$

Length of arc

radius $=21cm,\theta ={60}^o$

length $=\theta \times 2\pi r$

${360}^o$

$={60}^o\times 2\times \frac{22}{7}\times 21$

$=22cm$

Area of sector formed by arc$

Area $=\frac{\theta }{360}\times \pi r^2$

$=\frac{60}{360}\times \frac{22}{7}\times 21\times 21=231c{m}^2$

$\therefore$ length of arc $(\times 24)$

$\Rightarrow 22cm$

and Area of sector $(0\times 24)$

$\Rightarrow 231c{m}^2$