Chapter 12, Problem 23CR

To determine

To calculate: The length of a ${45}^{\circ }$ arc of a circle whose radius is $8\text{ units}$ .

Answer to Problem 23CR

The length of a ${45}^{\circ }$ arc of a circle with given radius of $8\text{ units}$ is $\text{6}\text{.283 units}$ .

Explanation of Solution

Given information: Given, angle of arc of a circle $\left(\theta \right)={45}^{\circ }$ and radius $\left(r\right)=8\text{ units}$ .

Formula used:

Length of arc of a circle $(S)=2\pi r\left(\frac{\theta }{{360}^{\circ }}\right)$ ………… (i)

where r = radius of a circle

  $\theta =$ angle subtended by an arc at the center of a circle

Calculation:

Let us calculate the length of an arc of a circle by using equation (i),

  $S=2\pi r\left(\frac{\theta }{{360}^{\circ }}\right)$

Substituting the given values $\theta ={45}^{\circ }$ and $r=8\text{ units }$ in above equation to get,

  $\begin{array}{l}S=2\times \pi \times 8\times \left(\frac{{45}^{\circ }}{{360}^{\circ }}\right)\\ S=2\times \pi \times 8\times \frac{1}{8}\\ S=2\pi \\ S=6.283\text{ units}\end{array}$

Hence, the length of a ${45}^{\circ }$ arc of a circle with given radius of $8\text{ units}$ is $\text{6}\text{.283 units}$ .