Find the area of the sector of a circle with radius 4 cm and of angle `30^(@)`. Also, find the area of the corresponding major sector. [Take `pi=3.14]`

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 1: Calculate the area of the entire circle
The formula for the area of a circle is given by:
\[ \text{Area of Circle} = \pi r^2 \]
Where \( r \) is the radius of the circle.

Given:
- Radius \( r = 4 \) cm
- \( \pi = 3.14 \)

Substituting the values:
\[ \text{Area of Circle} = 3.14 \times (4)^2 = 3.14 \times 16 = 50.24 \text{ cm}^2 \]

### Step 2: Calculate the area of the sector
The area of a sector of a circle can be calculated using the formula:
\[ \text{Area of Sector} = \frac{\theta}{360} \times \text{Area of Circle} \]
Where \( \theta \) is the angle of the sector in degrees.

Given:
- \( \theta = 30 \) degrees

Substituting the values:
\[ \text{Area of Sector} = \frac{30}{360} \times 50.24 \]
Calculating \( \frac{30}{360} \):
\[ \frac{30}{360} = \frac{1}{12} \]
Now substituting back:
\[ \text{Area of Sector} = \frac{1}{12} \times 50.24 = \frac{50.24}{12} \approx 4.1867 \text{ cm}^2 \]
Rounding to two decimal places, we get:
\[ \text{Area of Sector} \approx 4.19 \text{ cm}^2 \]

### Step 3: Calculate the area of the corresponding major sector
The area of the major sector can be found by subtracting the area of the minor sector from the area of the entire circle:
\[ \text{Area of Major Sector} = \text{Area of Circle} - \text{Area of Minor Sector} \]
Substituting the values:
\[ \text{Area of Major Sector} = 50.24 - 4.19 = 46.05 \text{ cm}^2 \]

### Final Answers:
- Area of the minor sector: \( 4.19 \text{ cm}^2 \)
- Area of the major sector: \( 46.05 \text{ cm}^2 \)