Find the area of a sector of a circle with radius 6 cm if angle of the sector is `60^@`

Explanation

To find the area of a sector of a circle with a radius of 6 cm and an angle of 60 degrees, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Formula for the Area of a Sector**:
The area of a sector of a circle can be calculated using the formula:
\[ \text{Area of Sector} = \frac{\theta}{360^\circ} \times \pi r^2 \]
where \( \theta \) is the angle of the sector in degrees, and \( r \) is the radius of the circle.

2. **Substitute the Given Values**:
Here, the radius \( r = 6 \) cm and the angle \( \theta = 60^\circ \). Substitute these values into the formula:
\[ \text{Area of Sector} = \frac{60}{360} \times \pi \times (6)^2 \]

3. **Simplify the Fraction**:
Simplify \( \frac{60}{360} \):
\[ \frac{60}{360} = \frac{1}{6} \]
So, the formula now becomes:
\[ \text{Area of Sector} = \frac{1}{6} \times \pi \times (6)^2 \]

4. **Calculate \( (6)^2 \)**:
Calculate \( (6)^2 \):
\[ (6)^2 = 36 \]
Now substitute this back into the equation:
\[ \text{Area of Sector} = \frac{1}{6} \times \pi \times 36 \]

5. **Multiply by \( \pi \)**:
Now, multiply:
\[ \text{Area of Sector} = \frac{36\pi}{6} = 6\pi \]

6. **Substitute the Value of \( \pi \)**:
Using \( \pi \approx \frac{22}{7} \):
\[ \text{Area of Sector} = 6 \times \frac{22}{7} = \frac{132}{7} \text{ cm}^2 \]

7. **Calculate the Decimal Value**:
Now, divide \( 132 \) by \( 7 \):
\[ \frac{132}{7} \approx 18.857 \text{ cm}^2 \]

8. **Final Answer**:
Therefore, the area of the sector is approximately:
\[ \text{Area of Sector} \approx 18.86 \text{ cm}^2 \]