https://file.aiquickdraw.com/mathbot/file/1725478737695n2gprgoz.jpg

The image shows a problem related to calculating the arc length of a sector of a circle. Here’s a step-by-step approach to solve the problem:

### Given:
- The angle of the sector \(\theta = 120^\circ\)
- The radius of the circle \(r = 8 \, \text{cm}\)

### To Find:
- The arc length \(L\) of the sector.

### Formula:
The arc length \(L\) of a sector is given by the formula:
\[
L = \frac{\theta}{360^\circ} \times 2\pi r
\]

### Substituting the values:
\[
L = \frac{120^\circ}{360^\circ} \times 2\pi \times 8 \, \text{cm}
\]
\[
L = \frac{1}{3} \times 2\pi \times 8 \, \text{cm}
\]
\[
L = \frac{16\pi}{3} \, \text{cm}
\]

### Numerical Value:
Approximating \(\pi \approx 3.14159\):
\[
L \approx \frac{16 \times 3.14159}{3} \, \text{cm}
\]
\[
L \approx 16.755 \, \text{cm}
\]

### Final Answer:
The arc length \(L\) is approximately **16.76 cm**.

Would you like more details on this calculation or have any other questions?

### Related Questions:
1. How would the arc length change if the radius was doubled?
2. What would be the arc length if the angle was 90 degrees instead of 120 degrees?
3. How can you calculate the area of the sector given the same angle and radius?
4. What is the formula to find the circumference of the entire circle?
5. How would the calculation change if the angle was in radians?

### Tip:
Remember, the arc length is a fraction of the circumference of the entire circle, with the fraction being determined by the angle over 360 degrees.

Calculate the arc length of a sector given the radius and angle as shown in the diagram.

Learn how to calculate the arc length of a sector with a 120-degree angle and an 8 cm radius. This problem covers key geometric concepts, including the formula for arc length and understanding the properties of a sector of a circle. Suitable for students in Grades 9-11.

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