Question

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

Answer 1

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:

Answer 2

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.

Answer 3

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.