Chapter 13.1, Problem 3MRE

To determine

To find: The distance that a point on the rim travels in one minite.

Answer to Problem 3MRE

The distance traveled by a point on the rim in one minute about $1696$ in.

Explanation of Solution

Given information:

The given velocity is $45$ rev/min.

  

Calculation:

Consider the velocity.

The distance traveled by a point on the rim in one revolution is equal to the circumference of the rim.

We know that circumference of a circle is $2\pi r$ .

Since diameter is, the radius will be $6$ .

Thus,

  $\begin{array}{c}2\pi r=2\pi \left(6\right)\\ =12\pi \end{array}$

The distance traveled in one revolution is $12\pi$ .

Thus the distance traveled in $45$ revolutions.

  $\left(12\pi \right)=540\pi$

Substitute $3.1416$ for $\pi$ , and simplify.

  $\begin{array}{c}540\pi =540\left(3.1416\right)\\ \approx 1696\end{array}$

Therefore, the distance traveled by a point on the rim in one minute about $1696$ in.