A wheel has a radius of 18 inches. Which distance, to the nearest inch, đoes the wheel travel when it .27 rotates through an angle of radians? 5 S= re 1) 45 2) 23 3) 13 4) 11
A wheel has a radius of 18 inches. Which distance, to the nearest inch, đoes the wheel travel when it .27 rotates through an angle of radians? 5 S= re 1) 45 2) 23 3) 13 4) 11
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
Related questions
Question
![### Problem Statement
A wheel has a radius of 18 inches. Which distance, to the **nearest inch**, does the wheel travel when it rotates through an angle of \(\frac{2\pi}{5}\) radians?
### Formula
To solve this problem, we use the formula for the arc length \(s\):
\[ s = r \theta \]
### Given Values
- **Radius (r):** 18 inches
- **Angle (\(\theta\)):** \(\frac{2\pi}{5}\) radians
### Calculation
Using the formula \(s = r \theta\):
\[ s = 18 \times \frac{2\pi}{5} \]
First, simplify the multiplication:
\[ s = 18 \times \frac{2\pi}{5} \]
\[ s = \frac{36\pi}{5} \]
Now, calculate \(\frac{36\pi}{5}\) using the approximation \(\pi \approx 3.14159\):
\[ s \approx \frac{36 \times 3.14159}{5} \]
\[ s \approx \frac{113.09724}{5} \]
\[ s \approx 22.619448 \]
Rounding to the nearest inch, the distance the wheel travels is approximately 23 inches.
### Answer Choices
1. 45
2. 23
3. 13
4. 11
**Correct Answer:** 2) 23](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F42779bdc-66e8-47e8-8a59-0cd69b39b8c3%2Fca18e489-703d-42f3-8c17-f6349d432135%2Fjyoteqi_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Problem Statement
A wheel has a radius of 18 inches. Which distance, to the **nearest inch**, does the wheel travel when it rotates through an angle of \(\frac{2\pi}{5}\) radians?
### Formula
To solve this problem, we use the formula for the arc length \(s\):
\[ s = r \theta \]
### Given Values
- **Radius (r):** 18 inches
- **Angle (\(\theta\)):** \(\frac{2\pi}{5}\) radians
### Calculation
Using the formula \(s = r \theta\):
\[ s = 18 \times \frac{2\pi}{5} \]
First, simplify the multiplication:
\[ s = 18 \times \frac{2\pi}{5} \]
\[ s = \frac{36\pi}{5} \]
Now, calculate \(\frac{36\pi}{5}\) using the approximation \(\pi \approx 3.14159\):
\[ s \approx \frac{36 \times 3.14159}{5} \]
\[ s \approx \frac{113.09724}{5} \]
\[ s \approx 22.619448 \]
Rounding to the nearest inch, the distance the wheel travels is approximately 23 inches.
### Answer Choices
1. 45
2. 23
3. 13
4. 11
**Correct Answer:** 2) 23
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