The volume of a sphere is 3,000pi m3. What is the surface area of the sphere to the nearest square meter?
(1 point)
To find the surface area of a sphere, we use the formula:
Surface area = 4 * pi * r^2,
where r is the radius of the sphere.
First, we need to find the radius of the sphere. We know that the volume of the sphere is 3,000pi m^3, so we can use the formula for the volume of a sphere:
Volume = (4/3) * pi * r^3 = 3,000pi,
which simplifies to:
r^3 = 3,000pi / [(4/3) * pi] = 3,000 / (4/3) = 2,250.
Taking the cube root of both sides, we find that the radius, r, is equal to 13.64 m (rounded to two decimal places).
Now, we can calculate the surface area of the sphere using the formula:
Surface area = 4 * pi * (13.64)^2 = 2,350.71 m^2.
Therefore, the surface area of the sphere to the nearest square meter is approximately 2,351 m^2.