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

Options

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

Answer

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

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

### Step 2: Substitute the given area into the formula.
We know the area \( A = 24.64 \, m^2 \). Thus, we can write:
\[ 24.64 = \pi r^2 \]

### Step 3: Use the value of \( \pi \).
For this calculation, we can use \( \pi \approx \frac{22}{7} \). So, we can rewrite the equation as:
\[ 24.64 = \frac{22}{7} r^2 \]

### Step 4: Solve for \( r^2 \).
To isolate \( r^2 \), we can multiply both sides by \( \frac{7}{22} \):
\[ r^2 = 24.64 \times \frac{7}{22} \]

### Step 5: Calculate \( r^2 \).
Now, let's perform the calculation:
\[ r^2 = 24.64 \times \frac{7}{22} = 24.64 \times 0.31818 \approx 7.84 \]

### Step 6: Find \( r \) by taking the square root of \( r^2 \).
Now, we take the square root of \( r^2 \):
\[ r = \sqrt{7.84} = 2.8 \, m \]

### Step 7: Write down the formula for the circumference of a circle.
The formula for the circumference \( C \) of a circle is:
\[ C = 2\pi r \]

### Step 8: Substitute the value of \( r \) into the circumference formula.
Now we substitute \( r = 2.8 \, m \) into the circumference formula:
\[ C = 2 \times \pi \times 2.8 \]

### Step 9: Use the value of \( \pi \) again.
Using \( \pi \approx \frac{22}{7} \):
\[ C = 2 \times \frac{22}{7} \times 2.8 \]

### Step 10: Calculate the circumference.
Now, let's calculate:
\[ C = 2 \times \frac{22}{7} \times 2.8 = \frac{44 \times 2.8}{7} = \frac{123.2}{7} \approx 17.6 \, m \]

### Final Answer:
The circumference of the circle is approximately \( 17.6 \, m \).

---