To determine the correct surface area of a sphere with a diameter of 10.4 inches, let's follow the calculations step-by-step:
1. Determine the Radius:
- The radius [tex]\( r \)[/tex] of a sphere is half of its diameter.
- Given the diameter [tex]\( d = 10.4 \)[/tex] inches,
[tex]\[
r = \frac{d}{2} = \frac{10.4}{2} = 5.2 \text{ inches}
\][/tex]
2. Calculate the Surface Area:
- The formula for the surface area [tex]\( S \)[/tex] of a sphere is [tex]\( 4\pi r^2 \)[/tex].
- Plugging in the radius length,
[tex]\[
S = 4 \pi (5.2)^2
\][/tex]
3. Simplify the Surface Area Calculation:
- Calculate [tex]\( (5.2)^2 \)[/tex]:
[tex]\[
(5.2)^2 = 27.04
\][/tex]
- Substitute [tex]\( 27.04 \)[/tex] back into the surface area formula:
[tex]\[
S = 4 \pi \times 27.04
\][/tex]
- Multiply [tex]\( 4 \)[/tex] by [tex]\( 27.04 \)[/tex]:
[tex]\[
S = 108.16 \pi
\][/tex]
Therefore, the surface area of the sphere is:
[tex]\[
108.16 \pi \text{ inches}^2
\][/tex]
So, the correct answer is:
[tex]\[
\boxed{D. \quad 108.16 \pi \text{ inches}^2}
\][/tex]
