Question

A bicycle wheel makes four revolutions. Determine how far the bicycle travels in feet. The diameter of the wheel is 24 in.​ (Use 3.14 for pi​.)
Question content area bottom
Part 1
The bicycle travels
  
enter your response here
▼
ft.
ft cubed .
ft squared .
​(Type a whole number or decimal rounded to the nearest tenth as​ needed.)

Answer 1

To determine how far the bicycle travels after making four revolutions, we need to calculate the circumference of the wheel first. The formula for the circumference \(C\) of a circle is given by:

\[
C = \pi \times d
\]

where \(d\) is the diameter of the circle.

Given:
- Diameter of the wheel \(d = 24\) inches
- Use \(\pi \approx 3.14\)

First, calculate the circumference in inches:

\[
C = 3.14 \times 24 = 75.36 \text{ inches}
\]

Next, we will convert the circumference from inches to feet since the final answer needs to be in feet. There are 12 inches in a foot, so:

\[
C = \frac{75.36 \text{ inches}}{12} \approx 6.28 \text{ feet}
\]

Now that we have the circumference in feet, we can calculate the distance traveled after four revolutions:

\[
\text{Distance} = \text{Circumference} \times \text{Number of Revolutions} = 6.28 \text{ feet} \times 4
\]

Now calculate the total distance:

\[
\text{Distance} = 6.28 \times 4 = 25.12 \text{ feet}
\]

Rounded to the nearest tenth, the distance the bicycle travels is:

\[
\text{Distance} \approx 25.1 \text{ feet}
\]

Thus, the final answer is:

\[
\text{The bicycle travels } 25.1 \text{ ft.}
\]