The circumference of a circular table is 88 m. Find its area.

Answer

To find the area of a circular table given its circumference, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the given information:**
The circumference of the circular table is given as 88 meters.

2. **Recall the formula for circumference:**
The formula for the circumference \( C \) of a circle is:
\[ C = 2 \pi r \]
where \( r \) is the radius of the circle.

3. **Set up the equation:**
Since the circumference is given as 88 meters, we can set up the equation:
\[ 2 \pi r = 88 \]

4. **Solve for the radius \( r \):**
To find the radius, we can rearrange the equation:
\[ r = \frac{88}{2 \pi} \]
Now, substituting \( \pi \) with \( \frac{22}{7} \):
\[ r = \frac{88}{2 \times \frac{22}{7}} = \frac{88 \times 7}{2 \times 22} \]
Simplifying this:
\[ r = \frac{88 \times 7}{44} = \frac{616}{44} = 14 \text{ meters} \]

5. **Calculate the area of the circle:**
The formula for the area \( A \) of a circle is:
\[ A = \pi r^2 \]
Substituting the value of \( r \) and \( \pi \):
\[ A = \frac{22}{7} \times (14)^2 \]
Calculating \( (14)^2 \):
\[ (14)^2 = 196 \]
Now substituting back:
\[ A = \frac{22}{7} \times 196 \]
Simplifying:
\[ A = \frac{22 \times 196}{7} \]
Dividing \( 196 \) by \( 7 \):
\[ 196 \div 7 = 28 \]
Thus:
\[ A = 22 \times 28 = 616 \text{ square meters} \]

6. **Final answer:**
The area of the circular table is \( 616 \, \text{m}^2 \).