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To solve the problem of finding the arc length of a circle with a central angle of \( 348^\circ \) and a radius of 23 meters, we use the formula for the arc length \( s \):

\[
s = \theta \cdot r
\]

where:
- \( \theta \) is the angle in radians, and
- \( r \) is the radius of the circle.

### Step 1: Convert degrees to radians
To convert the angle from degrees to radians, use the conversion factor \( \frac{\pi}{180} \):

\[
\theta = 348^\circ \times \frac{\pi}{180^\circ} = \frac{348\pi}{180} = \frac{29\pi}{15}
\]

### Step 2: Apply the arc length formula
Now substitute \( \theta = \frac{29\pi}{15} \) and \( r = 23 \) meters into the arc length formula:

\[
s = \left(\frac{29\pi}{15}\right) \times 23 = \frac{667\pi}{15} \text{ meters}
\]

Thus, the exact arc length is \( \frac{667\pi}{15} \) meters.

Would you like more details or have any questions? 

Here are some additional questions to consider:
1. How would the arc length change if the central angle were doubled?
2. What is the formula to find the circumference of the circle from the given radius?
3. Can you explain why the angle must be converted to radians in the formula?
4. How can the concept of arc length be applied in real-world scenarios like engineering or architecture?
5. How would you solve this problem if the radius of the circle were given in a different unit?

**Tip:** Always convert degrees to radians when working with formulas involving circular motion or arc lengths.

Find the length of an arc that subtends a central angle of 348° in a circle of radius 23 m.

Learn how to calculate the arc length of a circle with a central angle of 348° and a radius of 23 meters. The solution involves using the arc length formula, converting degrees to radians, and ensuring the answer is in terms of π. This problem is suitable for high school students in Grades 10-12.

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