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

Answer

To find the area of a sector of a circle with a radius of 4 cm and an angle of 30 degrees, 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 angle of the sector in degrees,
- \(r\) is the radius of the circle,
- \(\pi\) is approximately 3.14.

### Step-by-step solution:

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

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

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

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

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

6. **Substitute \(\frac{1}{12}\) into the formula**:
\[ \text{Area of sector} = \frac{1}{12} \times \pi \times 16 \]

7. **Calculate \(\frac{1}{12} \times 16\)**:
\[ \frac{1}{12} \times 16 = \frac{16}{12} = \frac{4}{3} \]

8. **Substitute \(\frac{4}{3}\) into the formula**:
\[ \text{Area of sector} = \frac{4}{3} \times \pi \]

9. **Substitute \(\pi = 3.14\)**:
\[ \text{Area of sector} = \frac{4}{3} \times 3.14 \]

10. **Calculate \(\frac{4 \times 3.14}{3}\)**:
\[ 4 \times 3.14 = 12.56 \]
\[ \text{Area of sector} = \frac{12.56}{3} \approx 4.1867 \, \text{cm}^2 \]

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