Question

Find the radius of circle in which a central angle of ${90}^{\circ }$ intercepts an arc of length $27.632\text{cm}$ (use $\pi =3.14$)

• A. $17.6\text{cm}$
• B. $8.8\text{cm}$
• C. $0.30\text{cm}$
• D. $0.60\text{cm}$

Answer 1

The correct option is A $17.6\text{cm}$

Here, $l=27.632\text{cm}$ and
$\theta ={90}^{\circ }={90}^{\circ }\times \frac{\pi }{180}=\frac{\pi }{2}\text{rad}$


We know , $\theta =\frac{l}{r}$
$r=\frac{l}{\theta }=\frac{27.632}{\frac{\pi }{2}}\text{cm}=\frac{27.632\times 2}{3.14}\text{cm}=17.6\text{cm}$