If the area of a sector of a circle of radius 2 cm is `pi` sq m, then what is the central angle of the sector ?

Answer

To find the central angle of a sector of a circle given the area of the sector and the radius, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the given values**:
- Radius (r) = 2 cm
- Area of the sector (A) = π sq m

2. **Recall the formula for the area of a sector**:
\[ A = \frac{\theta}{360} \times \pi r^2 \]
where \( \theta \) is the central angle in degrees.

3. **Substitute the known values into the formula**:
\[ \pi = \frac{\theta}{360} \times \pi \times (2)^2 \]

4. **Simplify the equation**:
- First, cancel π from both sides:
\[ 1 = \frac{\theta}{360} \times 4 \]
- This simplifies to:
\[ 1 = \frac{4\theta}{360} \]

5. **Multiply both sides by 360 to eliminate the fraction**:
\[ 360 = 4\theta \]

6. **Solve for θ**:
\[ \theta = \frac{360}{4} = 90 \text{ degrees} \]

### Final Answer:
The central angle of the sector is **90 degrees**.

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