To find out how much fabric is needed to cover the top of a circular table, we need to calculate the area of the circle.
The formula for the area \( A \) of a circle is:
\[ A = \pi r^2 \]
where \( r \) is the radius of the circle.
Given that the table is 6 feet across (the diameter), the radius \( r \) is:
\[ r = \frac{6 \text{ ft}}{2} = 3 \text{ ft} \]
Now, substituting the radius into the area formula:
\[ A = \pi (3 \text{ ft})^2 = \pi (9 \text{ ft}^2) \]
Calculating this gives:
\[ A \approx 3.14 \times 9 \approx 28.26 \text{ ft}^2 \]
Rounding to the nearest square foot, we find:
\[ A \approx 28 \text{ ft}^2 \]
So, you would need approximately 28 ft² of fabric to cover the top of the table.