Assertion (A) : In a circle of radius 6 cm, the angle of a sector `60^(@)` . Then area of sector is ` 18 (6)/(7) cm^(2)`
Reason (R) : Area of circle with radius r is ` pi r^(2)`

Options

A. Both A and R are true and R is the correct explanation of A
B. Both A and R are true and R is not correct explanation of A
C. A is true but R is false
D. A is false but R is true

Answer

To solve the problem, we need to find the area of a sector of a circle with a given radius and angle. Let's break it down step by step.

### Step-by-Step Solution:

1. **Identify the Given Values:**
- Radius (r) = 6 cm
- Angle of the sector (θ) = 60 degrees

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

3. **Substitute the Values into the Formula:**
Substitute \( r = 6 \) cm and \( \theta = 60 \) degrees into the formula:
\[ A = \frac{60}{360} \times \pi \times (6)^2 \]

4. **Simplify the Expression:**
First, simplify \( \frac{60}{360} \):
\[ \frac{60}{360} = \frac{1}{6} \]
Now substitute this back into the area formula:
\[ A = \frac{1}{6} \times \pi \times 36 \]

5. **Calculate the Area:**
Now calculate \( \pi \times 36 \):
\[ A = \frac{1}{6} \times 36\pi = 6\pi \]

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

7. **Final Result:**
The area of the sector is:
\[ A = \frac{132}{7} \text{ cm}^2 \approx 18.857 \text{ cm}^2 \]
This can be expressed as \( 18 \frac{6}{7} \text{ cm}^2 \).

### Conclusion:
The assertion that the area of the sector is \( 18 \frac{6}{7} \text{ cm}^2 \) is correct, and the reason given about the area of a circle is also valid.

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