Question:
Find the radius of a circle in which a central angle of $45^{\circ}$ intercepts an arc of length 33 cm. (Take $\pi=22 / 7$ )
Solution:
Angle in radians $=$ Angle in degrees $\times \frac{\pi}{180}$
$\theta=\frac{1}{r}$ where $\theta$ is central angle, $l=$ length of arc, $r=$ radius
Therefore angle $=45 \times \frac{\pi}{180}=\frac{\pi}{4}$
Now,
$r=\frac{1}{\theta}$
$=\frac{33}{\pi / 4}=\frac{132}{22 / 7}=\frac{924}{22}=42$
Therefore radius is $42 \mathrm{~cm}$