A sector has a central angle of `270^(@)` and a radius of 2. What is the area of the sector?

Answer

To find the area of a sector with a central angle of \(270^\circ\) and a radius of \(2\), 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 sector.

### Step-by-Step Solution:

1. **Identify the values**:
- Central angle, \(\theta = 270^\circ\)
- Radius, \(r = 2\)

2. **Substitute the values into the formula**:
\[ \text{Area} = \frac{270}{360} \times \pi \times (2^2) \]

3. **Calculate \(2^2\)**:
\[ 2^2 = 4 \]
So the equation becomes:
\[ \text{Area} = \frac{270}{360} \times \pi \times 4 \]

4. **Simplify \(\frac{270}{360}\)**:
- Both numbers can be divided by \(90\):
\[ \frac{270 \div 90}{360 \div 90} = \frac{3}{4} \]
Thus, the equation now is:
\[ \text{Area} = \frac{3}{4} \times \pi \times 4 \]

5. **Multiply \(\frac{3}{4}\) by \(4\)**:
\[ \frac{3 \times 4}{4} = 3 \]
Therefore, we have:
\[ \text{Area} = 3\pi \]

### Final Answer:
The area of the sector is \(3\pi\).

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