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Bot GPT-4o To determine the surface area of a sphere given its circumference, follow these steps:
1. **Find the radius (r):**
The formula for the circumference (C) of a sphere is:
\[
C = 2\pi r
\]
Given that the circumference is 40 ft:
\[
40 = 2\pi r
\]
Solving for \( r \):
\[
r = \frac{40}{2\pi} = \frac{40}{2 \times 3.14159} \approx \frac{40}{6.28318} \approx 6.3662 \text{ ft}
\]
2. **Calculate the surface area (A):**
The formula for the surface area of a sphere is:
\[
A = 4\pi r^2
\]
Using the radius found:
\[
A = 4\pi (6.3662)^2
\]
\[
A \approx 4 \times 3.14159 \times (6.3662)^2
\]
First, calculate \( (6.3662)^2 \):
\[
(6.3662)^2 \approx 40.5
\]
Then:
\[
A \approx 4 \times 3.14159 \times 40.5 \approx 4 \times 127.3 \approx 509.3 \text{ ft}^2
\]
Therefore, the surface area of the sphere is approximately \( 509.3 \text{ ft}^2 \).
So the correct answer is:
\[
509.3 \text{ ft}^2
\]