Question

Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.The diameter of a tire is 2.5 ft. Use this measurement to answer parts a and b. 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

We have a tire that is represented as a circle of diameter 2.5 ft.

A. The expression for the circumference of a tire in function of the diameter is pi times the diameter:

`C=\pi D\approx3.14\cdot2.5=7.85\text{ ft}`

B. In one rotation, the tire travels a distance equal to its circumference:

NOTE: you can visualize it like if we unroll the tire and measure the length. We get the circumference. In one rotation each of the points of the tire "touches" the ground one time, so the sum of the length is the circumference.

Then, in n rotations, the tire will travel C*n=7.85*n feet. We can calculate how many rotations correspond to 1 mile as:

`\begin{gathered} 7.85ft\cdot n=1\text{ mile}\cdot\frac{5280\text{ ft}}{1\text{ mile}}=5280\text{ ft} \\ n=\frac{5820\text{ ft}}{7.85\text{ ft}} \\ n\approx741.40\approx741 \end{gathered}`

Answer:

A) The circumference of the tire is 7.85 feet.

B) The tire has to rotate approximately 741 times to travel 1 mile.