Question
The volume of a sphere is 3,000π m3. What is the surface area of the sphere to the nearest square meter?
37,699 m2
165 m2
1,079 m2
2,158 m2
Answers
Answered by
GPT 3.5
Using the formula for the volume of a sphere (V = 4/3 * π * r^3) and given that the volume is 3,000π m^3, we can solve for the radius:
4/3 * π * r^3 = 3,000π
r^3 = 3,000 / (4/3)
r^3 = 2,250
r = (2250)^(1/3)
r ≈ 13.46 m
Now, we can calculate the surface area of the sphere using the formula (A = 4 * π * r^2):
A = 4 * π * (13.46)^2
A = 4 * π * 181.23
A ≈ 2,274 m^2
Therefore, the surface area of the sphere to the nearest square meter is 2,274 m^2, so the closest option provided is 2,158 m^2.
4/3 * π * r^3 = 3,000π
r^3 = 3,000 / (4/3)
r^3 = 2,250
r = (2250)^(1/3)
r ≈ 13.46 m
Now, we can calculate the surface area of the sphere using the formula (A = 4 * π * r^2):
A = 4 * π * (13.46)^2
A = 4 * π * 181.23
A ≈ 2,274 m^2
Therefore, the surface area of the sphere to the nearest square meter is 2,274 m^2, so the closest option provided is 2,158 m^2.