The volume of a sphere is 4,000pi m^3. What is the surface area of the sphere to the nearest square meter?
A. 2,614 m^2
B. 3,836 m^2
C. 1,307 m^2
D. 794 m^2
The formula for the volume of a sphere is V = (4/3)πr^3, where r is the radius of the sphere. We are given that the volume is 4,000π m^3, so we can set up the equation:
4,000π = (4/3)πr^3
Simplifying, we get:
r^3 = (3/4) x 4,000 = 3,000
Taking the cube root of both sides, we find:
r = 15
Now we can use the formula for the surface area of a sphere, which is A = 4πr^2. Plugging in the value we found for r, we get:
A = 4π(15)^2 = 2,826π
To the nearest square meter, this is approximately:
A ≈ 8,873 m^2
None of the answer choices match this value exactly, but the closest one is B. Therefore, the answer is B.