Question
A bicycle wheel makes four revolutions. Determine how far the bicycle travels in feet. The diameter of the wheel is 22 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.)
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.)
Answers
GPT-4o mini
To find out how far the bicycle travels after the wheel makes four revolutions, we first need to determine the circumference of the wheel. The circumference \( C \) of a circle is given by the formula:
\[
C = \pi \times d
\]
where \( d \) is the diameter of the circle.
### Step 1: Calculate the circumference of the wheel.
Given that the diameter of the wheel is \( 22 \) inches and \( \pi \approx 3.14 \):
\[
C = 3.14 \times 22 \, \text{inches}
\]
\[
C = 69.08 \, \text{inches}
\]
### Step 2: Convert the circumference from inches to feet.
Since there are 12 inches in a foot, we convert the circumference to feet:
\[
C = \frac{69.08}{12} \, \text{feet} \approx 5.757 \, \text{feet}
\]
### Step 3: Calculate the distance traveled for four revolutions.
If the wheel makes four revolutions, the total distance \( D \) traveled by the bicycle is:
\[
D = \text{Circumference} \times \text{Number of Revolutions}
\]
\[
D = 5.757 \, \text{feet} \times 4
\]
\[
D \approx 23.028 \, \text{feet}
\]
### Step 4: Round to the nearest tenth.
Rounding \( 23.028 \) to the nearest tenth gives:
\[
D \approx 23.0 \, \text{feet}
\]
### Final Answer:
The bicycle travels **23.0 feet**.
\[
C = \pi \times d
\]
where \( d \) is the diameter of the circle.
### Step 1: Calculate the circumference of the wheel.
Given that the diameter of the wheel is \( 22 \) inches and \( \pi \approx 3.14 \):
\[
C = 3.14 \times 22 \, \text{inches}
\]
\[
C = 69.08 \, \text{inches}
\]
### Step 2: Convert the circumference from inches to feet.
Since there are 12 inches in a foot, we convert the circumference to feet:
\[
C = \frac{69.08}{12} \, \text{feet} \approx 5.757 \, \text{feet}
\]
### Step 3: Calculate the distance traveled for four revolutions.
If the wheel makes four revolutions, the total distance \( D \) traveled by the bicycle is:
\[
D = \text{Circumference} \times \text{Number of Revolutions}
\]
\[
D = 5.757 \, \text{feet} \times 4
\]
\[
D \approx 23.028 \, \text{feet}
\]
### Step 4: Round to the nearest tenth.
Rounding \( 23.028 \) to the nearest tenth gives:
\[
D \approx 23.0 \, \text{feet}
\]
### Final Answer:
The bicycle travels **23.0 feet**.