Question

Question 16
A piece of wire 20 cm long is bent into the form of an arc of a circle subtending an angle of ${60}^{\circ }$ at its centre. Find the radius of the circle.

Answer 1

Length of arc of circle = 20 cm

Here, central angle $\theta ={60}^{\circ }$

$\therefore$ Length of arc $=\frac{\theta }{{360}^{\circ }}\times 2\pi r$

$\Rightarrow 20=\frac{\theta }{{360}^{\circ }}\times 2\pi r\Rightarrow \frac{20\times 6}{2\pi }=r$

$r=\frac{60}{\pi }cm$

Hence, the radius of circle is $\frac{60}{\pi }cm$