A manufacturer has created a spherical model of the Moon, using a scale ratio of 1:11580000. The model fits exactly into a cubic box with a volume of 27000 cm³. Determine the volume of the moon (in cubic km).
Cube of 27000 cu. cm has a side length of 30 cm. Thus, the diameter of the sphere is 30 cm, so its radius is 15 cm = 0.00015 km. Assuming the moon has a radius proportional via the scaling to the model's, and assuming the moon is "mostly spherical", we estimate the moon has a radius of $r =11580000\cdot 0.00015$ km. Then, we just plug that into the formula for volume of a sphere: $V = \dfrac{4}{3}\pi r^3$