Find the area of the sector of a circle with radius 7 cm and the angle at the centre is `30^(@)`.

Answer

To find the area of the sector of a circle with a radius of 7 cm and an angle of 30 degrees, we can follow these steps:

### Step 1: Write down the given information
- Radius (r) = 7 cm
- Angle at the center (θ) = 30 degrees

### Step 2: Use the formula for the area of a sector
The formula for the area of a sector is given by:
\[ \text{Area of sector} = \frac{\theta}{360} \times \pi r^2 \]

### Step 3: Substitute the values into the formula
Substituting the values of θ and r into the formula:
\[ \text{Area of sector} = \frac{30}{360} \times \pi \times (7)^2 \]

### Step 4: Simplify the fraction
First, simplify \(\frac{30}{360}\):
\[ \frac{30}{360} = \frac{1}{12} \]
Now substitute this back into the formula:
\[ \text{Area of sector} = \frac{1}{12} \times \pi \times (7)^2 \]

### Step 5: Calculate \(7^2\)
Calculate \(7^2\):
\[ 7^2 = 49 \]
Now substitute this value back into the formula:
\[ \text{Area of sector} = \frac{1}{12} \times \pi \times 49 \]

### Step 6: Substitute the value of \(\pi\)
Using \(\pi \approx \frac{22}{7}\):
\[ \text{Area of sector} = \frac{1}{12} \times \frac{22}{7} \times 49 \]

### Step 7: Simplify the expression
Now, simplify:
\[ \text{Area of sector} = \frac{22 \times 49}{12 \times 7} \]
Since \(49\) can be divided by \(7\):
\[ 49 \div 7 = 7 \]
So now we have:
\[ \text{Area of sector} = \frac{22 \times 7}{12} = \frac{154}{12} \]

### Step 8: Simplify \(\frac{154}{12}\)
Now simplify \(\frac{154}{12}\):
\[ \frac{154}{12} = \frac{77}{6} \text{ cm}^2 \]

### Final Answer
Thus, the area of the sector is:
\[ \text{Area} \approx 12.83 \text{ cm}^2 \]