Question:
A piece of wire 20 cm long is bent into the from of an arc of a circle, subtending an angle of 60° at its centre. Find the radius of the circle.
Solution:
Length of arc of circle = 20 cm
Here, $\quad$ central angle $\theta=60^{\circ}$
$\therefore$ Length of $\operatorname{arc}=\frac{\theta}{360^{\circ}} \times 2 \pi r$
$\Rightarrow$ $20=\frac{60^{\circ}}{360^{\circ}} \times 2 \pi r \Rightarrow \frac{20 \times 6}{2 \pi}=r$
$\therefore$ $r=\frac{60}{\pi} \mathrm{cm}$
Hence, the radius of circle is $\frac{60}{\pi} \mathrm{cm}$.