Area of the sector of a circle with radius 4 cm and of angle `30^(@)` is `:`

Options

A. `4.19cm^(2)`
B. `3.78 cm^(2)`
C. `5.25 cm^(2)`
D. None of these

Answer

To find the area of the sector of a circle with a radius of 4 cm and an angle of 30 degrees, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the formula for the area of a sector**:
The area \( A \) of a sector of a circle is given by the formula:
\[ A = \frac{\theta}{360} \times \pi r^2 \]
where \( \theta \) is the angle in degrees and \( r \) is the radius of the circle.

2. **Substitute the known values into the formula**:
Here, the radius \( r = 4 \) cm and the angle \( \theta = 30 \) degrees. Plugging these values into the formula gives:
\[ A = \frac{30}{360} \times \pi \times (4)^2 \]

3. **Calculate \( r^2 \)**:
First, calculate \( r^2 \):
\[ r^2 = 4^2 = 16 \]

4. **Simplify the fraction**:
Now, simplify \( \frac{30}{360} \):
\[ \frac{30}{360} = \frac{1}{12} \]

5. **Substitute back into the area formula**:
Now substitute \( r^2 \) and the simplified fraction back into the area formula:
\[ A = \frac{1}{12} \times \pi \times 16 \]

6. **Calculate the area**:
Using \( \pi \approx \frac{22}{7} \):
\[ A = \frac{1}{12} \times \frac{22}{7} \times 16 \]

7. **Perform the multiplication**:
Multiply \( \frac{22}{7} \) by \( 16 \):
\[ A = \frac{352}{7 \times 12} \]

8. **Simplify the expression**:
Now, calculate \( 7 \times 12 = 84 \):
\[ A = \frac{352}{84} \]

9. **Further simplify**:
Divide both the numerator and denominator by their greatest common divisor (GCD), which is 4:
\[ A = \frac{88}{21} \text{ cm}^2 \]

10. **Final result**:
The area of the sector is approximately:
\[ A \approx 4.19 \text{ cm}^2 \]