Question

The radius and length of an arc of a circle are 35 cm and 22 cm respectively The angle subtended by the arc at the centre of the circle is

• A. ${72}^{\circ }$
• B. ${45}^{\circ }$
• C. ${36}^{\circ }$
• D. ${40}^{\circ }$

Answer 1

The correct option is C ${36}^{\circ }$

Let $\theta$ be the required angle
Given radius $r=35cm$
length of an arc $=22cm$
$\Rightarrow \frac{2\pi r}{360}\times \theta =22$

$\Rightarrow \frac{2\times 22\times 35}{7\times 360}\times \theta =22$

$\therefore \theta =\frac{22\times 7\times 360}{2\times 22\times 35}={36}^{\circ }$