Find the radius and area of a circle, whose circumference is : 6.16 `m^(2)`

Answer

To find the radius and area of a 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 \( C = 6.16 \, \text{m} \).

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

3. **Substitute the given circumference into the formula:**
\[ 6.16 = 2\pi r \]

4. **Rearrange the formula to solve for \( r \):**
\[ r = \frac{C}{2\pi} = \frac{6.16}{2\pi} \]

5. **Use the value of \( \pi \):**
For calculations, we can use \( \pi \approx \frac{22}{7} \):
\[ r = \frac{6.16}{2 \times \frac{22}{7}} = \frac{6.16 \times 7}{2 \times 22} \]

6. **Calculate the value:**
\[ r = \frac{6.16 \times 7}{44} \]
First, calculate \( 6.16 \times 7 = 43.12 \):
\[ r = \frac{43.12}{44} \approx 0.98 \, \text{m} \]

7. **Now, calculate the area of the circle:**
The formula for the area \( A \) of a circle is given by:
\[ A = \pi r^2 \]

8. **Substitute the radius into the area formula:**
\[ A = \pi (0.98)^2 \]
Using \( \pi \approx \frac{22}{7} \):
\[ A = \frac{22}{7} \times (0.98 \times 0.98) \]

9. **Calculate \( 0.98 \times 0.98 \):**
\[ 0.98 \times 0.98 = 0.9604 \]
Thus,
\[ A = \frac{22}{7} \times 0.9604 \]

10. **Multiply to find the area:**
\[ A \approx 3.0184 \, \text{m}^2 \]

### Final Results:
- The radius of the circle is approximately \( 0.98 \, \text{m} \).
- The area of the circle is approximately \( 3.0184 \, \text{m}^2 \).