### Problem StatementA 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?### FormulaTo 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### CalculationUsing 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 Choices1. 452. 233. 134. 11**Correct Answer:** 2) 23

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Answered: A wheel has a radius of 18 inches.…

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

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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

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