If the circumference of a circle is 66 cm, then is its area is……………………….

Answer

To find the area of the circle given its circumference, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Information:**
- The circumference of the circle is given as 66 cm.

2. **Use the Formula for Circumference:**
- The formula for the circumference (C) of a circle is:
\[ C = 2\pi r \]
- Here, \( C = 66 \) cm.

3. **Substitute the Value of Circumference:**
- Substitute 66 cm into the formula:
\[ 66 = 2\pi r \]

4. **Solve for the Radius (r):**
- Rearranging the equation to find \( r \):
\[ r = \frac{66}{2\pi} \]
- Using \( \pi \approx \frac{22}{7} \):
\[ r = \frac{66}{2 \times \frac{22}{7}} = \frac{66 \times 7}{2 \times 22} \]

5. **Simplify the Expression:**
- Calculate the numerator and denominator:
\[ r = \frac{66 \times 7}{44} = \frac{462}{44} = \frac{231}{22} = 10.5 \text{ cm} \]

6. **Use the Radius to Find the Area:**
- The formula for the area (A) of a circle is:
\[ A = \pi r^2 \]
- Substitute \( r = 10.5 \) cm into the area formula:
\[ A = \pi (10.5)^2 \]

7. **Calculate \( (10.5)^2 \):**
- \( (10.5)^2 = 110.25 \)

8. **Substitute \( \pi \) and Calculate the Area:**
- Using \( \pi \approx \frac{22}{7} \):
\[ A = \frac{22}{7} \times 110.25 \]
- Calculate:
\[ A = \frac{22 \times 110.25}{7} \]
- \( 22 \times 110.25 = 2425.5 \)
- Now divide by 7:
\[ A \approx \frac{2425.5}{7} \approx 346.5 \text{ cm}^2 \]

### Final Answer:
The area of the circle is approximately **346.5 cm²**.

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