To find the surface area of a sphere when given its circumference, we can start by using the relationship between circumference and radius. The formula for the circumference (C) of a sphere is:
C = 2πr
where r is the radius. Given that the circumference is 40 ft, we can set up the equation:
40 = 2πr
Now, we can solve for r:
r = 40 / (2π) = 20 / π ≈ 6.366 ft
Next, we use the radius to find the surface area (A) of the sphere. The formula for the surface area of a sphere is:
A = 4πr²
Substituting the value of r we found:
A = 4π(20 / π)²
A = 4π(400 / π²)
A = 1600 / π ≈ 509.3 ft²
Finally, rounding to the nearest tenth, the surface area of the sphere is approximately 509.3 ft².