What will be the area of a circle whose circumference is 132 cm ?

Options

A. `693 cm^(2)`
B. `264 cm^(2)`
C. `5227 cm^(2)`
D. `1386 cm^(2)`

Answer

To find the area of a circle whose circumference is given as 132 cm, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the given information**:
- The circumference of the circle is given as 132 cm.

2. **Recall the formula for circumference**:
- The formula for the circumference (C) of a circle is given by:
\[ C = 2 \pi r \]
where \( r \) is the radius of the circle.

3. **Set up the equation**:
- Since we know the circumference, we can set up the equation:
\[ 2 \pi r = 132 \]

4. **Solve for the radius (r)**:
- To find \( r \), we can rearrange the equation:
\[ r = \frac{132}{2 \pi} \]
- Simplifying this gives:
\[ r = \frac{66}{\pi} \]

5. **Recall the formula for area**:
- The area (A) of a circle is given by:
\[ A = \pi r^2 \]

6. **Substitute the value of r into the area formula**:
- Now we substitute \( r = \frac{66}{\pi} \) into the area formula:
\[ A = \pi \left(\frac{66}{\pi}\right)^2 \]

7. **Calculate \( r^2 \)**:
- Squaring \( r \):
\[ r^2 = \left(\frac{66}{\pi}\right)^2 = \frac{66^2}{\pi^2} = \frac{4356}{\pi^2} \]

8. **Substitute \( r^2 \) back into the area formula**:
- Now substituting back, we have:
\[ A = \pi \cdot \frac{4356}{\pi^2} \]

9. **Simplify the area**:
- The \( \pi \) in the numerator and one \( \pi \) in the denominator cancel out:
\[ A = \frac{4356}{\pi} \]

10. **Calculate the numerical value of the area**:
- Using \( \pi \approx 3.14 \):
\[ A \approx \frac{4356}{3.14} \approx 1386 \text{ cm}^2 \]

### Final Answer:
The area of the circle is approximately **1386 cm²**.