Let's find the area of the circle step-by-step.
First, we know that the diameter of the circle is 10 inches.
1. Calculate the radius:
The radius is half of the diameter.
[tex]\[
\text{Radius} = \frac{\text{Diameter}}{2} = \frac{10 \text{ inches}}{2} = 5 \text{ inches}
\][/tex]
2. Calculate the area:
The formula to calculate the area of a circle is given by:
[tex]\[
\text{Area} = \pi r^2
\][/tex]
where [tex]\( r \)[/tex] is the radius.
3. Substitute the value of the radius:
[tex]\[
\text{Area} = \pi \times (5 \text{ inches})^2
\][/tex]
[tex]\[
\text{Area} = \pi \times 25 \text{ inches}^2
\][/tex]
4. Using the known value of [tex]\(\pi \approx 3.14159\)[/tex], the area can be computed as:
[tex]\[
\text{Area} \approx 3.14159 \times 25 \text{ in}^2 \approx 78.54 \text{ in}^2
\][/tex]
After rounding to the nearest tenth, the area is approximately [tex]\(78.5 \text{ in}^2\)[/tex].
Thus, the correct answer is:
A. [tex]\( 78.5 \text{ in}^2 \)[/tex]
