- Use the area formula for a circle: \(A = \pi r^2\).
- Substitute the given radius \(r = 24\) and \(\pi = 3.14\).
- Calculate \(A = 3.14 \times 24^2 = 3.14 \times 576 = 1808.64\).
- Round the final value to the nearest square inch, resulting in \(\boxed{1809 \text{ in.}^2}\).
Explanation
- Analyze the problem and identify the formula.
The problem asks for the area of a circular table top with a given radius. The radius is \(r = 24\) inches, and we are instructed to use the value \(\pi = 3.14\) for calculations. The area of a circle is calculated using the formula:
\[A = \pi r^2\]
Our goal is to find the area and round it to the nearest square inch to select the correct value from the given options.
- Calculate the area of the table top.
Using the given radius \(r = 24\), we first calculate the square of the radius:
\[r^2 = 24 \times 24 = 576 \text{ in.}^2\]
Next, we multiply this value by \(\pi \approx 3.14\) to find the area:
\[A = 3.14 \times 576\]
The result of this multiplication is \(1808.64\).
- Round the area and conclude.
The calculated area is \(1808.64 \text{ in.}^2\). Rounding this to the nearest whole number gives:
\[1808.64 \approx 1809 \text{ in.}^2\]
Comparing this result to the provided options, we see that \(1809 \text{ in.}^2\) is the correct choice.
The final answer is \(\boxed{1809 \text{ in.}^2}\).
Examples
Calculating the area of a circular object is a common task in interior design and home improvement. For example, if you are buying a circular rug for your living room, knowing the area of the rug helps you determine if it will fit the available floor space. If a rug has a radius of \(5\) feet, you can calculate its area as \(A = 3.14 \times 5^2 = 3.14 \times 25 = 78.5 \text{ ft.}^2\), ensuring you have enough room for it.