Find the area of a sector of a circle with an angle of `60^(@) ` and radius 7 cm `(" in cm"^(2))`

Options

A. `7 1/3`
B. `25 2/3`
C. `22 2/3`
D. `14 1/3 `

Answer

To find the area of a sector of a circle with a given angle and radius, we can use the formula:

\[ \text{Area of the sector} = \frac{\theta}{360} \times \pi r^2 \]

where:
- \(\theta\) is the angle of the sector in degrees,
- \(r\) is the radius of the circle,
- \(\pi\) is a constant approximately equal to \(3.14\) or \(\frac{22}{7}\).

### Step-by-Step Solution:

1. **Identify the given values**:
- Angle \(\theta = 60^\circ\)
- Radius \(r = 7 \, \text{cm}\)

2. **Substitute the values into the formula**:
\[ \text{Area of the sector} = \frac{60}{360} \times \pi \times (7)^2 \]

3. **Simplify the fraction**:
\[ \frac{60}{360} = \frac{1}{6} \]
So the formula becomes:
\[ \text{Area of the sector} = \frac{1}{6} \times \pi \times (7)^2 \]

4. **Calculate \(7^2\)**:
\[ 7^2 = 49 \]
Now the formula is:
\[ \text{Area of the sector} = \frac{1}{6} \times \pi \times 49 \]

5. **Substitute \(\pi\) with \(\frac{22}{7}\)**:
\[ \text{Area of the sector} = \frac{1}{6} \times \frac{22}{7} \times 49 \]

6. **Calculate the multiplication**:
- First, calculate \( \frac{22 \times 49}{7} \):
\[ 22 \times 49 = 1078 \]
\[ \frac{1078}{7} = 154 \]
- Now substitute back into the area formula:
\[ \text{Area of the sector} = \frac{1}{6} \times 154 \]

7. **Final calculation**:
\[ \text{Area of the sector} = \frac{154}{6} \approx 25.67 \, \text{cm}^2 \]

### Conclusion:
The area of the sector is approximately \(25.67 \, \text{cm}^2\).