Question

The radius of a circle is $$\displaystyle 30 $$ cm. The length of the arc of this circle whose chord is $$\displaystyle 30 $$ cm long, is

Answer 1

Correct option is B. $$\displaystyle 10\pi $$ cm

Let O be the centre of the circle and AB be the chord.Then, $$\displaystyle OA = OB = AB = 30 $$ cm.

$$\displaystyle \therefore \ \ \ \Delta OAB$$ is an equilateral triangle and therefore each of its angle is $$\displaystyle 60^0$$

$$\displaystyle \therefore \ \ \ \theta = \angle AOB = 60^0 = \Big( 60 \times \frac{\pi}{180} \Big)^c = \Big( \frac{\pi}{3}\Big)^c $$ and $$\displaystyle r = 30 $$ cm.

$$\displaystyle \therefore \ \ \ l = r \theta = \Big( 30 \times \frac{\pi}{3} \Big) $$ cm = $$\displaystyle (10 \pi )$$ cm.