What will be the radius of circle in which a central angle of 60° intercepts an arc of length 37.4 cm.

θ = 60°

$l=37.4 \mathrm{~cm}$

$r=?$

We know that,

$1^{\circ}=\left(\frac{\pi}{180^{\circ}}\right)^{\mathrm{R}}$

$\Rightarrow 60^{\circ}\left(\frac{\pi}{180^{\circ}} \times 60\right)^{\mathrm{R}}$

$\Rightarrow 60^{\circ}\left(\frac{\pi}{3}\right)^{\mathrm{R}}$

We know that,

$\theta=\frac{l}{r}$

$\Rightarrow \frac{\pi}{3}=\frac{37.4}{r}$

$\Rightarrow r=\frac{37.4 \times 3}{\pi}$

$r=\frac{37.4 \times 3 \times 7}{22}=1.7 \times 21=35.7 \mathrm{~cm}$