The circumference of a circle is 35.2 m. Find its area. 

Answer

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

### Step 1: Write down the formula for the circumference of a circle.
The formula for the circumference (C) of a circle is:
\[ C = 2 \pi r \]
where \( r \) is the radius of the circle and \( \pi \) is approximately \( \frac{22}{7} \) or \( 3.14 \).

### Step 2: Substitute the given circumference into the formula.
We know the circumference is \( 35.2 \) m, so we can set up the equation:
\[ 35.2 = 2 \pi r \]

### Step 3: Solve for the radius \( r \).
First, we can express \( \pi \) as \( \frac{22}{7} \):
\[ 35.2 = 2 \times \frac{22}{7} \times r \]

Now, simplify the equation:
\[ 35.2 = \frac{44}{7} r \]

To isolate \( r \), multiply both sides by \( \frac{7}{44} \):
\[ r = 35.2 \times \frac{7}{44} \]

### Step 4: Calculate the value of \( r \).
Now, perform the multiplication:
\[ r = \frac{35.2 \times 7}{44} \]

Calculating \( 35.2 \times 7 \):
\[ 35.2 \times 7 = 246.4 \]

Now divide by \( 44 \):
\[ r = \frac{246.4}{44} = 5.6 \, \text{m} \]

### Step 5: Write down the formula for the area of a circle.
The formula for the area (A) of a circle is:
\[ A = \pi r^2 \]

### Step 6: Substitute the value of \( r \) into the area formula.
Now substitute \( r = 5.6 \) m into the area formula:
\[ A = \pi (5.6)^2 \]

Using \( \pi \approx \frac{22}{7} \):
\[ A = \frac{22}{7} \times (5.6 \times 5.6) \]

### Step 7: Calculate \( (5.6)^2 \).
Calculating \( 5.6 \times 5.6 \):
\[ 5.6 \times 5.6 = 31.36 \]

### Step 8: Substitute back to find the area.
Now substitute \( 31.36 \) back into the area formula:
\[ A = \frac{22}{7} \times 31.36 \]

### Step 9: Calculate the area.
Now perform the multiplication:
\[ A = \frac{22 \times 31.36}{7} \]

Calculating \( 22 \times 31.36 \):
\[ 22 \times 31.36 = 689.92 \]

Now divide by \( 7 \):
\[ A = \frac{689.92}{7} \approx 98.56 \, \text{m}^2 \]

### Final Answer:
The area of the circle is approximately \( 98.56 \, \text{m}^2 \).

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