The area of a circle is `38.5cm^(2)` The circumference of the circle is

Options

A. 6.2cm
B. 12.1cm
C. 11cm
D. 22cm

Explanation

To find the circumference of the circle given its area, we can follow these steps:

### Step 1: Use 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: Set up the equation using the given area.
We know the area of the circle is \( 38.5 \, \text{cm}^2 \). Therefore, we can write:
\[ \pi r^2 = 38.5 \]

### Step 3: Solve for \( r^2 \).
To isolate \( r^2 \), we can divide both sides by \( \pi \):
\[ r^2 = \frac{38.5}{\pi} \]
Using \( \pi \approx \frac{22}{7} \) for calculation, we have:
\[ r^2 = \frac{38.5 \times 7}{22} \]

### Step 4: Calculate \( r^2 \).
Now, calculate the right side:
\[ r^2 = \frac{269.5}{22} \approx 12.25 \]

### Step 5: Find \( r \) by taking the square root.
Now, take the square root of both sides to find \( r \):
\[ r = \sqrt{12.25} = 3.5 \, \text{cm} \]

### 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 value of \( r \):
\[ C = 2 \times \pi \times 3.5 \]
Using \( \pi \approx \frac{22}{7} \):
\[ C = 2 \times \frac{22}{7} \times 3.5 \]

### Step 7: Calculate the circumference.
Now, calculate the circumference:
\[ C = 2 \times \frac{22 \times 3.5}{7} = 2 \times 22 = 44 \, \text{cm} \]

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

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