To find the approximate area of a circle with a diameter of 18 inches, follow these steps:
1. Find the radius:
The radius ([tex]\( r \)[/tex]) is half of the diameter. Given the diameter is 18 inches:
[tex]\[
r = \frac{18}{2} = 9 \text{ inches}
\][/tex]
2. Use the formula for the area of a circle:
The area [tex]\( A \)[/tex] of a circle is given by the formula:
[tex]\[
A = \pi r^2
\][/tex]
Plug in the radius:
[tex]\[
A \approx 3.14159 \times (9)^2
\][/tex]
3. Calculate the area:
[tex]\[
A \approx 3.14159 \times 81
\][/tex]
[tex]\[
A \approx 254.469
\][/tex]
4. Determine the closest option:
The options are:
- [tex]\( 1018 \, \text{in}^2 \)[/tex]
- [tex]\( 254 \, \text{in}^2 \)[/tex]
- [tex]\( 28.3 \, \text{in}^2 \)[/tex]
- [tex]\( 56.5 \, \text{in}^2 \)[/tex]
By comparing [tex]\( 254.469 \, \text{in}^2 \)[/tex] with the given options, the closest value is:
[tex]\[
254 \, \text{in}^2
\][/tex]
Therefore, the approximate area of the circle is:
[tex]\[
\boxed{254 \, \text{in}^2}
\][/tex]
