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

Answer

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

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

### Step 2: Set the area equal to the given value.
We know the area of the circle is \( 154 \, \text{cm}^2 \). Therefore, we can set up the equation:
\[ \pi r^2 = 154 \]

### Step 3: Substitute the value of \( \pi \).
We can use \( \pi \approx \frac{22}{7} \) for our calculations:
\[ \frac{22}{7} r^2 = 154 \]

### Step 4: Solve for \( r^2 \).
To eliminate the fraction, multiply both sides by \( 7 \):
\[ 22 r^2 = 154 \times 7 \]
Calculating the right side:
\[ 154 \times 7 = 1078 \]
So we have:
\[ 22 r^2 = 1078 \]
Now, divide both sides by \( 22 \):
\[ r^2 = \frac{1078}{22} \]
Calculating this gives:
\[ r^2 = 49 \]

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

### Step 6: Use the radius to find the circumference.
The formula for the circumference \( C \) of a circle is given by:
\[ C = 2 \pi r \]
Substituting the value of \( r \) and using \( \pi \approx \frac{22}{7} \):
\[ C = 2 \times \frac{22}{7} \times 7 \]

### Step 7: 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 \( 44 \, \text{cm} \).

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