...despite having more than a quarter the 2-dimensional size of Earth.
I think herein lies the problem; diameter is a 1-dimensional measurement, it's units are distance.
Let's rewrite 27.3% as 0.273. If that's the ratio of diameters, then the ratio of 2-dimensional areas should be (0.273)2 and the ratio of the volumes should be (0.273)3. Those numbers are 0....
It is all just geometry and mathematics.
The volume of a sphere is calculated according to this formula:
Volume = $(4/3) \times \pi \times r^3$
where $\pi$ = 3.14159..., and $r$ is the radius of the sphere.
The Earth radius is 6,371 km.
The Moon radius is 1,737 km.
We put the numbers into the formula and we get:
• The volume of Earth is 1,083,206,916,845....