The area of the sector with central angle `90^@` and radius `200 m` is

Options

A. 11400
B. 20000
C. 31400
D. 40000

Answer

To find the area of a sector with a central angle of \(90^\circ\) and a radius of \(200 \, m\), we can use the formula for the area of a sector:

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

where:
- \(\theta\) is the central angle in degrees,
- \(r\) is the radius of the circle,
- \(\pi\) is approximately \(3.14\).

### Step-by-step Solution:

1. **Identify the values**:
- Central angle \(\theta = 90^\circ\)
- Radius \(r = 200 \, m\)

2. **Substitute the values into the formula**:
\[ \text{Area of sector} = \frac{90}{360} \times \pi \times (200)^2 \]

3. **Simplify \(\frac{90}{360}\)**:
\[ \frac{90}{360} = \frac{1}{4} \]

4. **Calculate \(r^2\)**:
\[ (200)^2 = 40000 \]

5. **Substitute back into the formula**:
\[ \text{Area of sector} = \frac{1}{4} \times \pi \times 40000 \]

6. **Use \(\pi \approx 3.14\)**:
\[ \text{Area of sector} = \frac{1}{4} \times 3.14 \times 40000 \]

7. **Calculate \(\frac{1}{4} \times 40000\)**:
\[ \frac{40000}{4} = 10000 \]

8. **Now multiply by \(\pi\)**:
\[ \text{Area of sector} = 3.14 \times 10000 = 31400 \]

9. **Final result**:
\[ \text{Area of sector} = 31400 \, m^2 \]

### Final Answer:
The area of the sector with a central angle of \(90^\circ\) and radius \(200 \, m\) is \(31400 \, m^2\).