Question

In a circle a central angle of ${60}^o$ intercepts an arc of 15 inches. How many inches is the radius of the circle?

• A. $\frac{45}{\pi }$
• B. $\frac{\pi }{5}$
• C. 4
• D. $\frac{2\pi }{3}$
• E. not computable from given data

Answer 1

The correct option is A $\frac{45}{\pi }$

Let the radius$=r$

Length of arc$=l$

central angle $=\theta$

$l=r\theta$

In this problem

$\theta =\frac{\pi }{3}$

$l=15$ inch

$r=\frac{l}{\theta }=\frac{15}{\pi /3}=\frac{45}{\pi }$

So radius$=\frac{45}{\pi }$ inches.