Final answer:
The dimensions of the cube are approximately 47.70 meters on each side.
Step-by-step explanation:
To find the dimensions of a cube that has the same volume as a sphere with a radius of 30 meters, we need to calculate the volume of the sphere and then find the cube with the same volume.
The volume of the sphere can be calculated using the formula V = (4/3)πr³, where r is the radius. Plugging in the given radius, we get:
V_sphere = (4/3)π(30)³ = 113,097.34 m³
Now, to find the side length of the cube, we take the cube root of the volume of the sphere:
s_cube = ∛V_sphere = ∛113,097.34 = 47.70 m
Therefore, the cube has dimensions of approximately 47.70 meters on each side.