Question

The length of an arc of a sector of a circle of radius $r\text{units}$ and of central angle $\theta$ is:

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

Answer 1

The correct option is C $\frac{\theta }{{360}^{\circ }}\times 2\pi r$

We will use the unitary method to find the length of the arc having a central angle equal to $\theta$ and a radius of $r\text{units}$.

Length of an arc of a circle having central angle ${360}^{\circ }$ means the full circle is equal to $2\pi r$.

Length of an arc of a circle having central angle $1^{\circ }$ will be equal to $\frac{1}{{360}^{\circ }}\times 2\pi r$.

Length of an arc of a circle having central angle $\theta$ will be equal to $\frac{\theta }{{360}^{\circ }}\times 2\pi r$.

Hence, option $C$ is correct.