Question

Find the radius$\mathit{r}$ of the circle if an arc of length$\mathbf{15}\mathbf{}\mathbf{\text{m}}$ on the circle subtends a central angle of $\frac{\mathbf{5}\mathbf{\pi }}{\mathbf{6}}$.

Short answer

The radius $r$of the circle is $\mathbf{5}\mathbf{.73}$m.

Step-by-step solution

Step 1. Given information

The length of arc $S=20m$and the central angle $\theta =\frac{5\pi }{6}$.

The central angle in radians.

Step 2. Write the concept

Put the given value in the below formula and calculate the radius of circle:

$r=\frac{s}{\theta }$

Step 3. Determining the radius.

We know that-

$r=\frac{s}{\theta }$

Put the value in the above formula and calculate radius,

$$\begin{gathered} =\frac{15}{5\pi /6} \\ =15\times \frac{6}{5\pi } \\ =\frac{18}{\pi }\left(\because \pi =3.14\right) \\ =\frac{18}{3.14} \\ =5.73 \end{gathered}$$