Question

In a circle having radius r, an arc of a circle subtends an angle $\theta$ at the centre, then the length of arc l = ...............

• A. $\frac{\pi r^2\theta }{360}$
• B. $\pi r^2$
• C. $2\pi r$
• D. $\frac{\pi r\theta }{180}$

Answer 1

Answer: (D)

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

The length $L$ of an arc subtending an angle $\theta$ at the centre of the circle of radius $r$ is given by

$\frac{L}{\text{circumference}}=\frac{\theta }{2\pi }$

$\frac{L}{2\pi r}=\frac{\theta \pi }{180\times 2\pi }$

$⟹L=\frac{\pi r\theta }{180}$

Hence, option D is correct.