The volume of the sphere is 6,000 pi m to the 3rd power what is the surface area of the sphere to the nearest square meter
A. 18850 m2
B. 33m2
C.1090m2
D.3425m2
6,000 pi m^3 = (4/3) pi r^3
r^3 = 3,000 !!!!!!!!!!!!! I think not
I GET
r^3 = 18,000/4 = 4500
r = 16.5
r ≈ 15.9 m (rounded to one decimal place)
Now that we know the radius, we can use the formula for surface area of a sphere:
A = 4 pi r^2
A = 4 pi (15.9 m)^2
A ≈ 3,183.4 m^2
Rounding to the nearest square meter gives us:
A ≈ 3,183 m^2
I apologize for the error in my previous response. You are correct that the calculation of r^3 should give 4,500 instead of 3,000. Thank you for catching that mistake.
To find the surface area of a sphere, we can use the formula:
Surface Area = 4πr^2
where r is the radius of the sphere. However, we are only given the volume of the sphere, not its radius. So, we need to first find the radius using the given volume.
The formula to find the volume of a sphere is:
Volume = (4/3)πr^3
Given that the volume is 6000π m^3, we can set up the equation:
6000π = (4/3)πr^3
To solve for r, divide both sides of the equation by (4/3)π:
6000π / ((4/3)π) = r^3
Simplifying, we get:
r^3 = (3/4) * 6000
r^3 = 4500
Now, we can take the cube root of both sides to find r:
r = ∛4500
Using a calculator, we find that r ≈ 15.58 meters (rounded to two decimal places).
Now that we have the radius, we can calculate the surface area using the formula we mentioned earlier:
Surface Area = 4πr^2
Surface Area = 4π(15.58)^2
Surface Area ≈ 3049.32 square meters (rounded to two decimal places).
When rounded to the nearest square meter, the surface area of the sphere is approximately 3049 square meters.
Therefore, none of the given options (A, B, C, D) are correct.
We can use the formulas for volume and surface area of a sphere to solve this problem.
The formula for volume of a sphere is V = (4/3) pi r^3, where r is the radius.
If we set this equation equal to 6,000 pi m^3 and solve for r, we get:
6,000 pi m^3 = (4/3) pi r^3
r^3 = 3,000
r ≈ 15.9 m (rounded to one decimal place)
Now that we know the radius, we can use the formula for surface area of a sphere:
A = 4 pi r^2
A = 4 pi (15.9 m)^2
A ≈ 3,183.4 m^2
Rounding to the nearest square meter gives us:
A ≈ 3,183 m^2
The closest answer choice is C, 1090 m^2, but this is not a very close approximation. The correct answer is actually closer to A, 18,850 m^2.