The volume of a sphere is 3,000pi m3. What is the surface area of the sphere to the nearest square meter?
(1 point)
Responses
688 m2
688 m 2
1,079 m2
1,079 m 2
2,158 m2
2,158 m 2
3,167 m2
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 3000π m^3, we can solve for the radius (r) using the equation for the volume of a sphere:
Volume = (4/3)πr^3
3000π = (4/3)πr^3
Dividing both sides by (4/3)π, we get:
2250 = r^3
Taking the cube root of both sides, we find:
r = 12.68 m (rounded to two decimal places)
Now, substituting this radius into the equation for surface area, we can find the approximate surface area to the nearest square meter:
Surface Area = 4π(12.68)^2
Surface Area ≈ 2018.44 m^2
Therefore, the surface area of the sphere to the nearest square meter is 2018 m^2.