Chapter 4.1, Problem 52E

To determine

The length of the arc.

Answer to Problem 52E

The length of the arc is 7.85 meters

Explanation of Solution

Given information:Radius $r=3m$ , central angle $\theta ={150}^0$

Concept used:

The length of the arc of a circle with radius $r$ and central angle $\theta$ (in radians) is $s=r\theta$

Calculation:

Given central angle $\theta ={150}^0$

Convert into radians

  $\begin{array}{l}\theta ={150}^0=150(\frac{\pi }{180})rad\\ \theta =\frac{5\pi }{6}rad\end{array}$

Put $r=3m$ , $\theta =\frac{5\pi }{6}rad$ in $s=r\theta$

  $\begin{array}{l}s=3(\frac{5\pi }{6})=\frac{5\pi }{2}\\ s=7.85m\end{array}$

Therefore the length of the arc is 7.85 meters