The area of a circle is `616 cm^(2)`. Find its circumference

Answer

To solve the problem of finding the circumference of a circle when the area is given as 616 cm², we can follow these steps:

### Step-by-Step Solution:

1. **Understand 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 and \( \pi \) (Pi) is approximately \( \frac{22}{7} \).

2. **Set up the equation with the given area**:
We know the area of the circle is 616 cm². Therefore, we can write:
\[ \pi r^2 = 616 \]

3. **Substitute the value of Pi**:
Substitute \( \pi \) with \( \frac{22}{7} \):
\[ \frac{22}{7} r^2 = 616 \]

4. **Eliminate the fraction**:
To eliminate the fraction, multiply both sides by 7:
\[ 22 r^2 = 616 \times 7 \]

5. **Calculate \( 616 \times 7 \)**:
Calculate the right side:
\[ 616 \times 7 = 4312 \]
So, we have:
\[ 22 r^2 = 4312 \]

6. **Divide by 22**:
Now, divide both sides by 22 to solve for \( r^2 \):
\[ r^2 = \frac{4312}{22} \]

7. **Calculate \( \frac{4312}{22} \)**:
Performing the division:
\[ r^2 = 196 \]

8. **Find the radius \( r \)**:
To find \( r \), take the square root of both sides:
\[ r = \sqrt{196} = 14 \text{ cm} \]

9. **Use the radius to find the circumference**:
The formula for the circumference \( C \) of a circle is:
\[ C = 2 \pi r \]
Substitute \( r = 14 \) cm and \( \pi = \frac{22}{7} \):
\[ C = 2 \times \frac{22}{7} \times 14 \]

10. **Calculate the circumference**:
Simplifying the expression:
\[ C = 2 \times 22 \times 2 = 88 \text{ cm} \]

### Final Answer:
The circumference of the circle is \( 88 \text{ cm} \).

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