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 radius of the circle is 4.

Step-by-step solution

Step 1. Given information

The given length of the $\text{arc}=8$and the central angle in radian$\theta$ is$2\text{\hspace{0.17em}rad}$

Step 2. Explanation

We will use the formula of arc length,

$s=r\theta$

Step 3. Calculation

We know that,

$\begin{array}{l}\text{Thelengthof\hspace{0.17em}the\hspace{0.17em}arc\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}}s=r\theta \\ \text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}Therefore\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}}\frac{s}{\theta }=r\\ r=\frac{8}{2}\\ r=4\end{array}$