Find the area of a sector of a circle with radius 4 cm, if angle of the sector is `30^(@). (pi=3.14)`

Answer

To find the area of a 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 of the sector in degrees,
- \(r\) is the radius of the circle,
- \(\pi\) is a constant approximately equal to 3.14.

### Step-by-step Solution:

1. **Identify the given values:**
- Radius \(r = 4 \, \text{cm}\)
- Angle \(\theta = 30^\circ\)
- \(\pi = 3.14\)

2. **Substitute the values into the formula:**
\[ \text{Area of sector} = \frac{30}{360} \times 3.14 \times (4)^2 \]

3. **Calculate \( (4)^2 \):**
\[ (4)^2 = 16 \]

4. **Substitute \(16\) back into the equation:**
\[ \text{Area of sector} = \frac{30}{360} \times 3.14 \times 16 \]

5. **Simplify \(\frac{30}{360}\):**
\[ \frac{30}{360} = \frac{1}{12} \]

6. **Now substitute this back into the equation:**
\[ \text{Area of sector} = \frac{1}{12} \times 3.14 \times 16 \]

7. **Calculate \(3.14 \times 16\):**
\[ 3.14 \times 16 = 50.24 \]

8. **Now substitute this back into the equation:**
\[ \text{Area of sector} = \frac{50.24}{12} \]

9. **Perform the division:**
\[ \text{Area of sector} = 4.18666667 \approx 4.19 \, \text{cm}^2 \]

### Final Answer:
The area of the sector is approximately \(4.19 \, \text{cm}^2\).