Chapter 6.1, Problem 60E

To determine

To find: the number of radians that a spot on the tire will travel during the trip.

Answer to Problem 60E

10937.5 radians

Explanation of Solution

Given information:

  $\begin{array}{l}\text{Distance travelled by bike}\left(s\right)=3.5km=350000cm\\ \text{Radius of tire }\left(r\right)=32cm\end{array}$

Calculation:

The distance travelled by the bike is the length of an arc $\left(s\right)$ and number of radians that a spot on the tire travelled during the trip is the central angle $\left(\theta \right)$ .

The central angle $\left(\theta \right)$ of an arc will be evaluated as follows:

  $\begin{array}{c}s=r\theta \\ 350000cm=\left(32cm\right)\theta \left[\text{Put the value of }s\text{ and }r\right]\\ \theta =\frac{350000cm}{32cm}\\ =10937.5\text{ radians}\end{array}$

Thus the radius of the circle is 10937.5 radians.