The area of a circle is `24.64 m^2`. The circumference of the circle is

Options

A. 14.64 m
B. 16.36 m
C. 17.60 m
D. 18.40 m

Answer

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

### Step 1: Write 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 \( 24.64 \, m^2 \). Therefore, we can write:
\[ \pi r^2 = 24.64 \]

### Step 3: Use the value of \( \pi \).
For this calculation, we will use \( \pi \approx 3.14 \). Thus, we can rewrite the equation as:
\[ 3.14 r^2 = 24.64 \]

### Step 4: Solve for \( r^2 \).
To find \( r^2 \), we divide both sides of the equation by \( 3.14 \):
\[ r^2 = \frac{24.64}{3.14} \]
Calculating this gives:
\[ r^2 \approx 7.84 \]

### Step 5: Find the radius \( r \).
To find \( r \), we take the square root of \( r^2 \):
\[ r = \sqrt{7.84} \]
Calculating this gives:
\[ r \approx 2.8 \, m \]

### Step 6: Write 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 we can substitute \( r = 2.8 \, m \) into the circumference formula:
\[ C = 2 \times 3.14 \times 2.8 \]

### Step 8: Calculate the circumference.
Calculating this gives:
\[ C \approx 6.28 \times 2.8 \approx 17.584 \, m \]

### Final Answer:
The circumference of the circle is approximately \( 17.584 \, m \).

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