Question

The radius of a circle is 30 cm. Find the length of an arc of this circle, if the length of the chord of the arc is 30 cm.

Answer 1

We have,

OA = OB = radius of circle = 30 cm = 0.3 m

AB = chord AB = 30 cm = 0.3 m

Arc AB = $\widehat{AB}$ = 1 (say)

Now, $\Delta AOB$ is equilateral triangle as OA = OB = AB = 30 cm

$\therefore \angle AOB={60}^{\circ }=\frac{\pi }{3}\text{radian}$

$\therefore \theta =\frac{\text{arc}}{\text{radius}}$

$\Rightarrow \frac{\pi }{3}=\frac{1}{0.3}$

$\Rightarrow l=\frac{0.3}{3}\pi =0.1\pi m$

$\therefore l=arcAB=10\pi cm$