16. The tires on a bicycle have a diameter of 70 centimeters. About how far does the bicycle travel each time the tires make 10 complete revolutions? A. 11 meters B. 22 meters C. 38 meters D. 44 meters
16. The tires on a bicycle have a diameter of 70 centimeters. About how far does the bicycle travel each time the tires make 10 complete revolutions? A. 11 meters B. 22 meters C. 38 meters D. 44 meters
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
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Question
![**Question:**
The tires on a bicycle have a diameter of 70 centimeters. About how far does the bicycle travel each time the tires make 10 complete revolutions?
A. 11 meters
B. 22 meters
C. 38 meters
D. 44 meters
---
**Explanation:**
To solve this problem, we need to calculate the circumference of the tire and then determine the total distance traveled in 10 revolutions.
1. **Calculate the circumference of the tire:**
- The formula for the circumference of a circle is \( C = \pi d \), where \( d \) is the diameter.
- Given: Diameter (\( d \)) = 70 centimeters.
Therefore:
\[
C = \pi \times 70 \text{ centimeters} \approx 3.14 \times 70 \text{ centimeters} = 219.8 \text{ centimeters}
\]
2. **Convert the circumference to meters:**
- Since 1 meter = 100 centimeters:
\[
219.8 \text{ centimeters} = \frac{219.8}{100} \text{ meters} = 2.198 \text{ meters}
\]
3. **Calculate the total distance for 10 revolutions:**
\[
\text{Total distance} = \text{Circumference} \times \text{Number of revolutions} = 2.198 \text{ meters} \times 10 = 21.98 \text{ meters}
\]
4. **Round the total distance to the nearest meter:**
\[
21.98 \text{ meters} \approx 22 \text{ meters}
\]
**Answer:**
B. 22 meters](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7acfa03c-ce8c-4cd5-a52f-d1ef747591d8%2F065112f0-b1d7-41e0-9066-39869ed36a7e%2Fc64hnze_processed.png&w=3840&q=75)
Transcribed Image Text:**Question:**
The tires on a bicycle have a diameter of 70 centimeters. About how far does the bicycle travel each time the tires make 10 complete revolutions?
A. 11 meters
B. 22 meters
C. 38 meters
D. 44 meters
---
**Explanation:**
To solve this problem, we need to calculate the circumference of the tire and then determine the total distance traveled in 10 revolutions.
1. **Calculate the circumference of the tire:**
- The formula for the circumference of a circle is \( C = \pi d \), where \( d \) is the diameter.
- Given: Diameter (\( d \)) = 70 centimeters.
Therefore:
\[
C = \pi \times 70 \text{ centimeters} \approx 3.14 \times 70 \text{ centimeters} = 219.8 \text{ centimeters}
\]
2. **Convert the circumference to meters:**
- Since 1 meter = 100 centimeters:
\[
219.8 \text{ centimeters} = \frac{219.8}{100} \text{ meters} = 2.198 \text{ meters}
\]
3. **Calculate the total distance for 10 revolutions:**
\[
\text{Total distance} = \text{Circumference} \times \text{Number of revolutions} = 2.198 \text{ meters} \times 10 = 21.98 \text{ meters}
\]
4. **Round the total distance to the nearest meter:**
\[
21.98 \text{ meters} \approx 22 \text{ meters}
\]
**Answer:**
B. 22 meters
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