The area of a circle is 154 sq. cm. Find its circumference.

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 the area \( A = 154 \) sq. cm. Therefore, we can write:
\[ \pi r^2 = 154 \]

### Step 3: Use the value of \( \pi \).
For calculations, we can use \( \pi \approx \frac{22}{7} \). Substituting this value into the equation gives:
\[ \frac{22}{7} r^2 = 154 \]

### Step 4: Solve for \( r^2 \).
To isolate \( r^2 \), multiply both sides by \( \frac{7}{22} \):
\[ r^2 = 154 \times \frac{7}{22} \]
Now, calculate \( \frac{154}{22} \):
\[ \frac{154}{22} = 7 \]
So,
\[ r^2 = 7 \times 7 = 49 \]

### Step 5: Find the radius \( r \).
Taking the square root of both sides gives:
\[ r = \sqrt{49} = 7 \text{ cm} \]

### Step 6: 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 7: Substitute the value of \( r \) into the circumference formula.
Substituting \( r = 7 \) cm and \( \pi \approx \frac{22}{7} \):
\[ C = 2 \times \frac{22}{7} \times 7 \]

### Step 8: Simplify the expression.
The \( 7 \) in the numerator and denominator cancels out:
\[ C = 2 \times 22 = 44 \text{ cm} \]

### Final Answer:
The circumference of the circle is \( 44 \) cm.

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