Question

The length of an arc which subtends an angle $\theta$ at the centre of a circle of radius r is

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

Answer 1

The correct option is A $\frac{\mathrm{\pi r\theta }}{180}$

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 the radius of the circle.

For an angle of $\theta$, the arc length will be $\frac{\theta }{360}\times 2\pi r=\frac{\theta }{180}\times \pi r$.