Question

Find the length of the arc in terms of $\pi$ that subtends an angle of ${30}^{\circ }$ at the centre of a circle of radius $4$ cm.

Answer 1

$\Rightarrow$ $\theta ={30}^o$ and $r=4cm$

$\Rightarrow$ Length of an arc $=\frac{\theta }{{360}^o}\left(2\pi r\right)$

Where, $\theta$ is angle subtended at a center.

$2\pi r$ is circumference of a circle.

$\Rightarrow$ Length of an arc $=\frac{{30}^o}{{360}^o}\times 2\pi \times 4$

$\Rightarrow$ Length of an arc $=\frac{2\pi \times 4}{12}$

$\therefore$ Length of an arc $=\frac{2\pi }{3}$