Sure, let's detail the step-by-step solution to finding the surface area of a sphere with a given radius of [tex]\(2\sqrt{2}\)[/tex] feet.
### Step-by-Step Solution:
1. Identify the formula for the surface area of a sphere:
The formula for the surface area [tex]\(A\)[/tex] of a sphere is given by:
[tex]\[ A = 4\pi r^2 \][/tex]
2. Substitute the given radius into the formula:
Here, [tex]\(r = 2\sqrt{2}\)[/tex] feet.
3. Calculate [tex]\(r^2\)[/tex]:
[tex]\[
r^2 = (2\sqrt{2})^2 = 2^2 \cdot (\sqrt{2})^2 = 4 \cdot 2 = 8
\][/tex]
4. Plug [tex]\(r^2\)[/tex] into the surface area formula:
[tex]\[
A = 4 \pi r^2 = 4 \pi \cdot 8 = 32\pi
\][/tex]
5. Calculate the numerical value of [tex]\(32\pi\)[/tex]:
Using [tex]\(\pi \approx 3.1416\)[/tex]:
[tex]\[
A = 32 \pi \approx 32 \times 3.1416 \approx 100.53096
\][/tex]
Hence, the surface area of the sphere is approximately [tex]\(100.53096\)[/tex] square feet.
Among the given options, the result closest to [tex]\(100.53096\)[/tex] is:
- [tex]\(100.5\)[/tex] square feet.
Thus, the correct answer is:
[tex]\[
\boxed{100.5 \text{ square feet}}
\][/tex]
