The problem in the image asks to "Find the Arc Length" given the following information:

• $r = 4$ inches (radius)
• $\theta = \frac{2\pi}{3}$ radians (central angle)

Formula for Arc Length:

The formula to find the arc length $s$ of a circle is: $s = r \cdot \theta$ where:

• $r$ is the radius of the circle,
• $\theta$ is the central angle in radians.

Substituting the given values:

$s = 4 \cdot \frac{2\pi}{3}$ $s = \frac{8\pi}{3} \text{ inches}$

So, the arc length is $\frac{8\pi}{3}$ inches, which is approximately $8.38$ inches.

Let me know if you want further details or explanations!

Related Questions:

1. What is the relationship between the radius and arc length in a unit circle?
2. How does the arc length change if the central angle is given in degrees instead of radians?
3. Can you calculate the sector area for the same radius and angle?
4. How would you find the arc length if the radius was halved?
5. What happens to the arc length if the central angle becomes $\pi$ radians?

Tip: Always ensure the angle is in radians when applying the arc length formula $s = r \theta$.