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

Options

A. 44 cm
B. 110 cm
C. 84 cm
D. 24 cm

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 of the circle is \( 154 \, \text{cm}^2 \). So we can set up the equation:
\[ \pi r^2 = 154 \]

### Step 3: Use the value of \( \pi \).
For this problem, we can use \( \pi \approx \frac{22}{7} \) or \( 3.14 \). We will use \( \frac{22}{7} \) for this calculation:
\[ \frac{22}{7} r^2 = 154 \]

### Step 4: Solve for \( r^2 \).
To isolate \( r^2 \), multiply both sides of the equation by \( 7 \) to eliminate the fraction:
\[ 22 r^2 = 154 \times 7 \]
Calculating \( 154 \times 7 \):
\[ 154 \times 7 = 1078 \]
So,
\[ 22 r^2 = 1078 \]
Now, divide both sides by \( 22 \):
\[ r^2 = \frac{1078}{22} \]
Calculating \( \frac{1078}{22} \):
\[ r^2 = 49 \]

### Step 5: Find the radius \( r \).
To find \( r \), take the square root of \( r^2 \):
\[ r = \sqrt{49} = 7 \, \text{cm} \]

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