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Find the surface area of a sphere with a radius of [tex]\( 2\sqrt{2} \)[/tex] feet.

A. 94.5 square feet
B. 35.5 square feet
C. 25.1 square feet
D. 100.5 square feet


Sagot :

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]
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