Question

What is the length of an arc of a circle of radius $8$ units that subtends a central angle of radian measure $\frac{11\mathrm{\pi }}{12}$?

Answer 1

Find the length of an arc of a circle:

Given, that the radius of a circle is $8\mathrm{units}$ and the angle subtended at the center is $\frac{11\mathrm{\pi }}{12}$.

The arc's length can be determined as follows,

$\mathrm{arc}\mathrm{length}=\mathrm{circumference}\times \frac{\mathrm{angle}\mathrm{subtended}\mathrm{at}\mathrm{centre}}{2\mathrm{\pi }}$

Where, $\mathrm{circumference}=2\mathrm{\pi r}$

Substitute the values in the above formula:

$\begin{array}{rcl}\text{arc length}& =& 2\pi \times 8\times \frac{\frac{11\pi }{12}}{2\pi }\\ & =& 2\pi \times 8\times \frac{\frac{11\pi }{12}}{2\pi }\\ & =& \frac{8\times 11\pi }{12}\\ & =& \frac{88\pi }{12}\\ & \approx & 23.038\text{units}\end{array}$

Therefore, the length of an arc of a circle is approximately $23.038\mathit{}\mathrm{units}$.