Question

The volume of a sphere is 3,000π m3. What is the surface area of the sphere to the nearest square meter?

A. 688 m^2
B. 1,079 m^2
C. 2,158 m^2
D. 3,167 m^2

Answer 1

To find the surface area of a sphere, we can use the formula:

Surface Area = 4πr^2

Given that the volume of the sphere is 3,000π m^3, we can find the radius (r) using the formula for the volume of a sphere:

Volume = (4/3)πr^3
3,000π = (4/3)πr^3
r^3 = (3,000 * 3) / 4
r^3 = 2,250
r = ∛2,250
r ≈ 12.08 m

Now, we can calculate the surface area of the sphere:

Surface Area = 4π(12.08)^2
Surface Area ≈ 1,157.464 m^2

Rounded to the nearest square meter, the surface area of the sphere is 1,157 m^2.

Therefore, the closest option is B. 1,079 m^2.