Answer :
To find the surface area of a sphere with radius [tex]$r = 2\sqrt{2}$[/tex] feet, we use the formula for the surface area of a sphere:
[tex]$$
S = 4\pi r^2.
$$[/tex]
Step 1: Compute the square of the radius.
Given [tex]$r = 2\sqrt{2}$[/tex], we have
[tex]$$
r^2 = \left(2\sqrt{2}\right)^2 = 4 \times 2 = 8.
$$[/tex]
Step 2: Substitute [tex]$r^2$[/tex] into the surface area formula.
Substitute [tex]$r^2 = 8$[/tex] into the formula:
[tex]$$
S = 4\pi \times 8 = 32\pi.
$$[/tex]
Step 3: Approximate the numerical value.
Using the approximation [tex]$\pi \approx 3.1416$[/tex], we find
[tex]$$
S \approx 32 \times 3.1416 \approx 100.5309 \text{ square feet}.
$$[/tex]
Rounded to one decimal place, the surface area is approximately [tex]$100.5$[/tex] square feet.
Thus, the surface area of the sphere is [tex]$\boxed{100.5\text{ square feet}}$[/tex].
[tex]$$
S = 4\pi r^2.
$$[/tex]
Step 1: Compute the square of the radius.
Given [tex]$r = 2\sqrt{2}$[/tex], we have
[tex]$$
r^2 = \left(2\sqrt{2}\right)^2 = 4 \times 2 = 8.
$$[/tex]
Step 2: Substitute [tex]$r^2$[/tex] into the surface area formula.
Substitute [tex]$r^2 = 8$[/tex] into the formula:
[tex]$$
S = 4\pi \times 8 = 32\pi.
$$[/tex]
Step 3: Approximate the numerical value.
Using the approximation [tex]$\pi \approx 3.1416$[/tex], we find
[tex]$$
S \approx 32 \times 3.1416 \approx 100.5309 \text{ square feet}.
$$[/tex]
Rounded to one decimal place, the surface area is approximately [tex]$100.5$[/tex] square feet.
Thus, the surface area of the sphere is [tex]$\boxed{100.5\text{ square feet}}$[/tex].
