Question

Find the radius $\mathit{r}$of the circle if an arc of length 20 cm on the circle subtends a central angle of ${\mathbf{50}}^{\mathbf{\circ }}$.

Short answer

The radius of the circle is$\mathbf{\text{r}}\mathbf{=}\mathbf{22}\mathbf{.}\mathbf{92}\mathbf{\text{cm}}$.

Step-by-step solution

Step 1. Given information.

The length of arc$s=20m$ and the central angle$\theta ={50}^{\circ }$

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.

The radius of the circle:

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

Put the given value in the above formula:

$$\begin{gathered} =\frac{20}{5}\times \pi \times 18 \\ =\frac{72}{\pi }\left(\because \pi =3.14\right) \\ =22.92\text{cm} \end{gathered}$$