Question

Find the length of an arc of a circle of radius $3cm$, if the angle subtended at the centre is $30^{\circ }$. $(\pi =3.14)$

• A. $1.50cm$
• B. $1.35cm$
• C. $1.57cm$
• D. $1.20cm$

Answer 1

Answer: (C)

Let $l$ be the length of the arc. We know that,
Angle $\theta =\frac{l}{r}$, where $\theta$ is in radian.
Given, $r=3cm$,
$\theta =30^{\circ }=30\times \frac{\pi }{180}=\frac{\pi }{6}$ rad
On putting the values of $r$ and $\theta$, we get
$\frac{\pi }{6}=\frac{l}{3}$
$\Rightarrow l=\frac{\pi }{2}=\frac{3.14}{2}$
$=1.57cm$