Question

Find the length $\mathit{s}$of the circular arc, the radius $\mathit{r}$of the circle, or the central angle $\theta$, as indicated.

Short answer

The Length of the arc is $\frac{\mathbf{15}\mathbf{\pi }}{\mathbf{2}}$.

Step-by-step solution

Step 1. Given information

The given radius $=9$and the central angle in radian $\theta$is $\frac{5\pi }{6}$

Step 2. Explanation

We will use the formula of arc length,

$s=r\theta$

Step 3. CalculationWe know that,

$\begin{array}{l}\text{Thelengthof\hspace{0.17em}the\hspace{0.17em}arc\hspace{0.17em}}s=r\theta \\ s=9.\frac{5\pi }{6}\\ =\frac{15\pi }{2}\text{\hspace{0.17em}radian}\end{array}$