Question

a bicycle wheel has a radius of 7 in. if the bicycle travels 470 ft., how many revolutions does the wheel make? round your answer to two decimal places.

Explanation:

Step1: Convert radius to feet

The radius of the wheel is 7 inches. Since 1 foot = 12 inches, we convert inches to feet: $r = \frac{7}{12}$ ft.

Step2: Calculate circumference of the wheel

The formula for the circumference of a circle is $C = 2\pi r$. Substituting $r = \frac{7}{12}$ ft, we get $C = 2\pi\times\frac{7}{12}=\frac{7\pi}{6}$ ft.

Step3: Calculate number of revolutions

The distance traveled is 470 ft. The number of revolutions $n$ is the total distance divided by the circumference: $n=\frac{470}{\frac{7\pi}{6}}=\frac{470\times6}{7\pi}=\frac{2820}{7\pi}$.

Step4: Compute the value

Using $\pi\approx3.1416$, we calculate $\frac{2820}{7\times3.1416}\approx\frac{2820}{21.9912}\approx128.23$.

Answer:

128.23