Answer:
A. The circumference of the tire is approximately 7.854 feet.
B. The tire rotates about 672 times to travel 1 mile.
Step-by-step explanation:
A. The circunference ([tex]s[/tex]), measured in feet, in terms of diameters is defined by the following formula:
[tex]s = \pi \cdot D[/tex] (1)
Where [tex]D[/tex] is the diameter of the tire, measured in feet.
If we know that [tex]D = 2.5\,ft[/tex], then the circunference of the tire is:
[tex]s = \pi\cdot (2.5\,ft)[/tex]
[tex]s \approx 7.854\,ft[/tex]
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 ([tex]n[/tex]), no unit, associated to the distance travelled is calculated by this expression:
[tex]n = \frac{s}{\pi\cdot D}[/tex] (2)
If we know that [tex]s = 5280\,ft[/tex] and [tex]D = 2.5\,ft[/tex], then the number of revolutions done by the tire to travel 1 mile is:
[tex]n = \frac{5280\,ft}{\pi\cdot (2.5\,ft)}[/tex]
[tex]n \approx 672.270[/tex]
The tire rotates about 672 times to travel 1 mile.
