Chapter 12, Problem 3STP

To determine

To calculate: Arc length of the given circle.

Answer to Problem 3STP

(A) $7.1$ ft

Explanation of Solution

Given information: The diameter of the circle is given as $68$ feet. Also, the angle made by the wheel when it takes a passenger is $12°$

Formula used: We know that $1°=\left(\frac{\pi }{180°}\right)rad$ . And the arc length $s=r\alpha$ . Also, the radius of the circle $r=\frac{d}{2}$ . Here, $d$ is the diameter of the circle and the angle $\alpha$ is in radian.

Calculation: Find the radius of the circle.

  $\begin{array}{l}r=\frac{d}{2}\\ r=\frac{68}{2}\\ r=34\end{array}$

Now, when it takes the passenger, the wheel will travel the arc length.

Find the arc length

  $\begin{array}{l}s=r\alpha \\ s=34\times 12°\times \left(\frac{\pi }{180°}\right)\\ s=2.267\pi \\ s=2.267\times 3.141\\ s=7.120\\ s=7.1\end{array}$