A piece of wire 20 cm long is bent into

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 $\frac{60}{\pi} \mathrm{cm}$.