Question

Radius of a circle is $28$ cm. What is the angle subtended by an arc of length $17.6$ at the centre?

• A. ${10}^o$
• B. ${30}^o$
• C. ${36}^o$
• D. ${45}^o$

Answer 1

The correct option is C ${36}^o$

Let the angle subtended by the arc at the centre be $\theta$,
$r=28\text{cm}\text{length of arc}=17.6\text{cm}$

We know,
$\text{Length of arc}=\frac{\theta }{{360}^o}\times 2\pi r$

So,$17.6=\frac{\theta }{{360}^o}\times 2\times \frac{22}{7}\times 28$

$\Rightarrow \frac{17.6\times {360}^o\times 7}{2\times 22\times 28}=\theta$

$\theta ={36}^o$

Hence, option$\left(c\right)$ correct.