Find the length of the arc of a sector of a circle with radius 6 cm whose angle is `60^(@)`.

Answer

To find the length of the arc of a sector of a circle with a given radius and angle, we can use the formula:

\[ \text{Length of arc} = \frac{\theta}{360^\circ} \times 2\pi r \]

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

### Step-by-Step Solution:

1. **Identify the given values**:
- Radius (\(r\)) = 6 cm
- Angle (\(\theta\)) = 60°

2. **Substitute the values into the formula**:
\[ \text{Length of arc} = \frac{60}{360} \times 2\pi \times 6 \]

3. **Simplify the fraction**:
\[ \frac{60}{360} = \frac{1}{6} \]

4. **Substitute the simplified value back into the formula**:
\[ \text{Length of arc} = \frac{1}{6} \times 2\pi \times 6 \]

5. **Calculate the multiplication**:
\[ \text{Length of arc} = \frac{1}{6} \times 12\pi = 2\pi \]

6. **Final answer**:
The length of the arc is \(2\pi\) cm.