To find the volume of the cylinder, we first need to find the radius of the sphere.
The formula for the volume of a sphere is given by:
V_sphere = (4/3) * π * r^3
We can rearrange the formula to solve for the radius, r:
r = cuberoot((3 * V_sphere) / (4 * π))
Given that the volume of the sphere is 48 cubic meters, we can substitute this value into the formula:
r = cuberoot((3 * 48) / (4 * π))
r ≈ 1.8905 meters
Now we can find the volume of the cylinder, using the formula:
V_cylinder = π * r^2 * h
Given that the height of the cylinder is equal to the diameter of the sphere, which is twice the radius, we have:
h = 2 * r ≈ 2 * 1.8905 ≈ 3.781 meters
Substituting values into the volume formula:
V_cylinder = π * (1.8905^2) * 3.781
V_cylinder ≈ π * 3.5715 * 3.781
V_cylinder ≈ π * 13.5022
V_cylinder ≈ 42.4762 cubic meters
Therefore, the volume of the cylinder is approximately 42.4762 cubic meters.