The radius of the circle is 14cm and the area of its sector will be if the angle of sector be `60^(@)` `:`

Options

A. `( 308) /( 3) cm^(3)`
B. `(308) /(3) cm`
C. `( 308) /( 3) cm^(2)`
D. `( 22)/( 3) cm^(2)`

Answer

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

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

Where:
- \(\theta\) is the angle of the sector in degrees,
- \(r\) is the radius of the circle.

### Step-by-Step Solution:

1. **Identify the given values:**
- Radius \(r = 14 \text{ cm}\)
- Angle \(\theta = 60^\circ\)

2. **Substitute the values into the formula:**
\[ \text{Area of the sector} = \frac{60}{360} \times \pi \times (14)^2 \]

3. **Simplify the fraction:**
\[ \frac{60}{360} = \frac{1}{6} \]
So the formula now becomes:
\[ \text{Area of the sector} = \frac{1}{6} \times \pi \times (14)^2 \]

4. **Calculate \(14^2\):**
\[ 14^2 = 196 \]
Now substitute this value back into the equation:
\[ \text{Area of the sector} = \frac{1}{6} \times \pi \times 196 \]

5. **Multiply \(\frac{196}{6}\):**
\[ \frac{196}{6} = 32.67 \text{ (approximately)} \]
Therefore, we have:
\[ \text{Area of the sector} \approx 32.67 \pi \]

6. **Use the value of \(\pi\):**
Using \(\pi \approx \frac{22}{7}\):
\[ \text{Area of the sector} \approx 32.67 \times \frac{22}{7} \]

7. **Calculate the final area:**
\[ \text{Area of the sector} \approx 32.67 \times 3.14 \approx 102.67 \text{ cm}^2 \]

### Final Answer:
The area of the sector is approximately \(102.67 \text{ cm}^2\).