Find circumference of the circle, whose area is 24.64 `m^(2)`.

Answer

To find the circumference of a circle whose area is given as 24.64 m², 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: 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 calculations, we can use \( \pi \approx \frac{22}{7} \). Substituting this into the equation gives:
\[ 24.64 = \frac{22}{7} r^2 \]

### 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 \( r^2 \).
Calculating the right side:
\[ r^2 = 24.64 \times \frac{7}{22} = 24.64 \times 0.3182 \approx 7.84 \]

### Step 6: Find the radius \( r \).
Now, take the square root of both sides to find \( r \):
\[ r = \sqrt{7.84} = 2.8 \, m \]

### Step 7: 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 \( r \):
\[ C = 2 \times \frac{22}{7} \times 2.8 \]

### Step 8: Calculate the circumference.
First, simplify:
\[ C = 2 \times \frac{22 \times 2.8}{7} \]
Calculating \( 22 \times 2.8 = 61.6 \):
\[ C = 2 \times \frac{61.6}{7} \approx 2 \times 8.8 = 17.6 \, m \]

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

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