Question

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The diameter of a tire is 2.5 ft. Use this measurement to answer parts a and b. Show all work to receive full credit. A. Find the circumference of the tire.
B. About how many times will the tire have to rotate to travel 1 mile? (1 mile = 5,280 ft)

Answer 1

A. The circumference of the tire is approximately 7.854 feet.

B. The tire rotates about 672 times to travel 1 mile.

Explanation:

A. The circunference (
`s`), measured in feet, in terms of diameters is defined by the following formula:

`s = \pi \cdot D` (1)

Where
`D` is the diameter of the tire, measured in feet.

If we know that
`D = 2.5\,ft`, then the circunference of the tire is:

`s = \pi\cdot (2.5\,ft)`

`s \approx 7.854\,ft`

The circumference of the tire is approximately 7.854 feet.

B. The value found in A. represents the distance travelled by the tire per revolution. Then, the number of revolutions (
`n`), no unit, associated to the distance travelled is calculated by this expression:

`n = (s)/(\pi\cdot D)` (2)

If we know that
`s = 5280\,ft` and
`D = 2.5\,ft`, then the number of revolutions done by the tire to travel 1 mile is:

`n = (5280\,ft)/(\pi\cdot (2.5\,ft))`

`n \approx 672.270`

The tire rotates about 672 times to travel 1 mile.