Question

How many revolutions will a car wheel ofdiameter 30 in. make as the car travels a distance of one mile?

Short answer

The car wheel will make 672.6 revolutions per mile.

Step-by-step solution

Step 1. Given information.

$D=30$in.

Step 2. Write the concept.

To find revolutions will a car wheel of diameter 30 in. make as the car travels a distance of one mile.

First find the total travel distance in one revolution by using below formula:

$C=\pi D$

Where $D=$diameter of car wheel

$C=$circumference (total travel distance in one revolution)

Step 3. Determining the values.

The total travel distance in one revolution by car wheel is:

$C=\mathrm{\pi }d$

Put given values in the formula:

$C=3.1430$

$C=94.2$in

Now convert unit of total distance into inches:

We know that

$1mile=5280ft$;

$1foot=12inches$;

$1mile=5280ft=5280\times 12$

$1mile=63360inches$.

Now, divide total distance by travel distance in one revolution:

$\frac{63360}{94.2}=672.6$revolution per mile