To find the area of a circle with a diameter of 12.6 inches, follow these steps:
1. Find the radius: The radius of a circle is half of its diameter. Therefore, the radius [tex]\( r \)[/tex] is:
[tex]\[
r = \frac{\text{diameter}}{2} = \frac{12.6}{2} = 6.3 \, \text{inches}
\][/tex]
2. Use the formula for the area of a circle: The formula to calculate the area [tex]\( A \)[/tex] of a circle is:
[tex]\[
A = \pi r^2
\][/tex]
Here, [tex]\(\pi\)[/tex] (pi) is given as 3.14.
3. Substitute the radius and value of [tex]\(\pi\)[/tex] into the formula:
[tex]\[
A = 3.14 \times (6.3)^2
\][/tex]
4. Calculate the square of the radius:
[tex]\[
(6.3)^2 = 39.69
\][/tex]
5. Multiply by [tex]\(\pi\)[/tex]:
[tex]\[
A = 3.14 \times 39.69 = 124.6266
\][/tex]
6. Round to the nearest hundredth: The area calculated is 124.6266 square inches. Rounded to the nearest hundredth, this becomes:
[tex]\[
A \approx 124.63 \, \text{in}^2
\][/tex]
Thus, the area of the circle with a diameter of 12.6 inches is:
[tex]\[
\boxed{124.63 \, \text{in}^2}
\][/tex]
