The area of the sector of a circle whose radius is 6 metre when the angle at the centre is ` 42^(@)` is

Options

A. `13 . 2 m^(2)`
B. ` 14 . 2 m^(2)`
C. ` 13 . 4 m^(2)`
D. ` 14 . 4 m^(2)`

Answer

To find the area of the sector of a circle, we can use the formula:

\[ \text{Area of sector} = \frac{\theta}{360} \times \pi r^2 \]

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

### Step-by-Step Solution:

1. **Identify the given values**:
- Radius \(r = 6\) meters
- Angle \(\theta = 42\) degrees

2. **Substitute the values into the formula**:
\[ \text{Area of sector} = \frac{42}{360} \times \pi \times (6)^2 \]

3. **Calculate \(6^2\)**:
\[ 6^2 = 36 \]

4. **Substitute \(36\) back into the formula**:
\[ \text{Area of sector} = \frac{42}{360} \times \pi \times 36 \]

5. **Simplify \(\frac{42}{360}\)**:
\[ \frac{42}{360} = \frac{7}{60} \]

6. **Now substitute this back into the area formula**:
\[ \text{Area of sector} = \frac{7}{60} \times \pi \times 36 \]

7. **Multiply \( \frac{7}{60} \times 36\)**:
\[ \frac{7 \times 36}{60} = \frac{252}{60} = 4.2 \]

8. **Now multiply by \(\pi\)**:
\[ \text{Area of sector} = 4.2\pi \]

9. **Using \(\pi \approx 3.14\)**, calculate the area:
\[ \text{Area of sector} \approx 4.2 \times 3.14 \approx 13.188 \]

10. **Final result**:
\[ \text{Area of sector} \approx 13.19 \text{ m}^2 \]

### Conclusion:
The area of the sector of the circle is approximately \(13.19 \text{ m}^2\).