Question

What is the length of an arc which subtends angle $\theta$ (degrees) at the center in a circle of radius r?

• A. $\frac{\pi r\theta }{180}$
• B. $\frac{\pi r\theta }{360}$
• C. $\frac{\pi r\theta }{60}$
• D. $\frac{\pi r\theta }{90}$

Answer 1

The correct option is A

$\frac{\pi r\theta }{180}$

For an angle of ${360}^{\circ }$ subtended at the centre, the arc length is nothing but the circumference of circle that is 2$\pi r$, where $r$ is circle radius. For an angle of $\theta$, the arc length will be $\frac{\theta }{360}\times 2\pi r$