Find the circumference of a circle whose area is `6.16cm^(2)`

Answer

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

### Step 1: Write down the formula for the area of a circle.
The area \( A \) of a circle is given by the formula:
\[ A = \pi r^2 \]
where \( r \) is the radius of the circle.

### Step 2: Substitute the given area into the formula.
We know that the area \( A \) is \( 6.16 \, \text{cm}^2 \). Therefore, we can set up the equation:
\[ 6.16 = \pi r^2 \]

### Step 3: Use the value of \( \pi \).
We can use \( \pi \approx \frac{22}{7} \) for our calculations. Substituting this value into the equation, we have:
\[ 6.16 = \frac{22}{7} r^2 \]

### Step 4: Solve for \( r^2 \).
To isolate \( r^2 \), we multiply both sides by \( \frac{7}{22} \):
\[ r^2 = 6.16 \times \frac{7}{22} \]

### Step 5: Calculate \( r^2 \).
Calculating the right side:
\[ r^2 = 6.16 \times \frac{7}{22} = 6.16 \times 0.31818 \approx 1.96 \]

### Step 6: Find \( r \) by taking the square root.
Now, take the square root of both sides to find \( r \):
\[ r = \sqrt{1.96} \approx 1.4 \, \text{cm} \]

### Step 7: Write down the formula for the circumference of a circle.
The circumference \( C \) of a circle is given by the formula:
\[ C = 2\pi r \]

### Step 8: Substitute the value of \( r \) into the circumference formula.
Now substitute \( r = 1.4 \, \text{cm} \) into the circumference formula:
\[ C = 2 \times \pi \times 1.4 \]
Using \( \pi \approx \frac{22}{7} \):
\[ C = 2 \times \frac{22}{7} \times 1.4 \]

### Step 9: Calculate the circumference.
Calculating this gives:
\[ C = \frac{44}{7} \times 1.4 = \frac{44 \times 1.4}{7} = \frac{61.6}{7} \approx 8.8 \, \text{cm} \]

### Final Answer:
The circumference of the circle is approximately \( 8.8 \, \text{cm} \).

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