Question

A bicycle tire has a radius of 8 inches. How many feet will the bicycle travel after 15 revolutions of the tire?

Answer 1

To determine how far a bicycle will travel after 15 revolutions of the tire, we first need to calculate the circumference of the tire. The formula for the circumference \( C \) of a circle is given by:

\[
C = 2 \pi r
\]

where \( r \) is the radius of the circle.

Given that the radius \( r \) of the bicycle tire is 8 inches, we can calculate the circumference:

\[
C = 2 \pi (8) = 16\pi \text{ inches}
\]

Next, we can find the distance traveled after 15 revolutions by multiplying the circumference of the tire by the number of revolutions:

\[
\text{Distance} = \text{Circumference} \times \text{Number of Revolutions}
\]
\[
\text{Distance} = 16\pi \times 15 = 240\pi \text{ inches}
\]

Now we need to convert the distance from inches to feet. There are 12 inches in a foot, so we convert the distance as follows:

\[
\text{Distance in feet} = \frac{240\pi \text{ inches}}{12} = 20\pi \text{ feet}
\]

Finally, we can compute the numerical value using \( \pi \approx 3.14 \):

\[
20\pi \approx 20 \times 3.14 = 62.8 \text{ feet}
\]

Thus, the bicycle will travel approximately:
\[
\boxed{62.8 \text{ feet}}
\] after 15 revolutions of the tire.