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Answer :
To find the surface area of a sphere with radius [tex]$r$[/tex], we use the formula:
[tex]$$
\text{Surface Area} = 4 \pi r^2.
$$[/tex]
Here, the radius is given as [tex]$r = 2\sqrt{2}$[/tex] feet.
1. First, calculate [tex]$r^2$[/tex]:
[tex]$$
r^2 = \left(2\sqrt{2}\right)^2 = 2^2 \cdot (\sqrt{2})^2 = 4 \cdot 2 = 8.
$$[/tex]
2. Substitute [tex]$r^2 = 8$[/tex] into the surface area formula:
[tex]$$
\text{Surface Area} = 4 \pi \times 8 = 32\pi.
$$[/tex]
3. Evaluating [tex]$32\pi$[/tex] numerically gives approximately:
[tex]$$
32\pi \approx 100.5 \text{ square feet}.
$$[/tex]
Thus, the surface area of the sphere is approximately [tex]$100.5$[/tex] square feet.
[tex]$$
\text{Surface Area} = 4 \pi r^2.
$$[/tex]
Here, the radius is given as [tex]$r = 2\sqrt{2}$[/tex] feet.
1. First, calculate [tex]$r^2$[/tex]:
[tex]$$
r^2 = \left(2\sqrt{2}\right)^2 = 2^2 \cdot (\sqrt{2})^2 = 4 \cdot 2 = 8.
$$[/tex]
2. Substitute [tex]$r^2 = 8$[/tex] into the surface area formula:
[tex]$$
\text{Surface Area} = 4 \pi \times 8 = 32\pi.
$$[/tex]
3. Evaluating [tex]$32\pi$[/tex] numerically gives approximately:
[tex]$$
32\pi \approx 100.5 \text{ square feet}.
$$[/tex]
Thus, the surface area of the sphere is approximately [tex]$100.5$[/tex] square feet.
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