The area of a circle is `346.5 cm^(2)`. Find its circumference (in cm).

Options

A. 132
B. 38
C. 66
D. 76

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 \( 346.5 \, \text{cm}^2 \). So we can set up the equation:
\[ \pi r^2 = 346.5 \]

### Step 3: Use the value of \( \pi \).
For calculations, we can use \( \pi \approx \frac{22}{7} \). Substituting this into the equation gives:
\[ \frac{22}{7} r^2 = 346.5 \]

### Step 4: Solve for \( r^2 \).
To isolate \( r^2 \), multiply both sides by \( \frac{7}{22} \):
\[ r^2 = 346.5 \times \frac{7}{22} \]
Calculating the right side:
\[ r^2 = 346.5 \times \frac{7}{22} = 110.25 \]

### Step 5: Take the square root to find \( r \).
Now, take the square root of both sides to find \( r \):
\[ r = \sqrt{110.25} = 10.5 \, \text{cm} \]

### 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.
Now substitute \( r = 10.5 \, \text{cm} \) into the circumference formula:
\[ C = 2 \times \frac{22}{7} \times 10.5 \]

### Step 8: Calculate the circumference.
Calculating this gives:
\[ C = \frac{44}{7} \times 10.5 = \frac{462}{7} \approx 66 \, \text{cm} \]

### Final Answer:
The circumference of the circle is \( 66 \, \text{cm} \).

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