If the area of a circle is 154 `cm^(2)`, then its circumference is :

Options

A. 11 cm
B. 22 cm
C. 44 cm
D. 55 cm

Answer

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

### Step-by-Step Solution:

1. **Identify the given area of the circle**:
The area of the circle is given as \( 154 \, \text{cm}^2 \).

2. **Use the formula for the area of a circle**:
The formula for the area \( A \) of a circle is:
\[ A = \pi r^2 \]
where \( r \) is the radius of the circle.

3. **Set up the equation**:
Substitute the given area into the formula:
\[ 154 = \pi r^2 \]

4. **Solve for \( r^2 \)**:
Rearranging the equation gives:
\[ r^2 = \frac{154}{\pi} \]
Using \( \pi \approx \frac{22}{7} \), we can substitute this value:
\[ r^2 = \frac{154 \times 7}{22} \]

5. **Calculate \( r^2 \)**:
First, calculate \( 154 \times 7 \):
\[ 154 \times 7 = 1078 \]
Now divide by 22:
\[ r^2 = \frac{1078}{22} = 49 \]

6. **Find the radius \( r \)**:
To find \( r \), take the square root of \( r^2 \):
\[ r = \sqrt{49} = 7 \, \text{cm} \]

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

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

9. **Simplify the expression**:
The \( 7 \) in the numerator and denominator cancels out:
\[ C = 2 \times 22 = 44 \, \text{cm} \]

10. **Final answer**:
The circumference of the circle is \( 44 \, \text{cm} \).