The Moon has 27.3% of the Earth's radius/diameter but only 2% of the Earth's volume. I don't quite get it why the Moon's volume is that small despite having more than a quarter the 2-dimensional size of Earth. Compared to the Earth, does the Moon really have 2% of the Earth's 3-dimensional size? Why is it like this with the Moon and other bodies of similar diameters?
...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 0.0745 and 0.0203 respectively.
So the next question is why with a volume of 2% of Earth that The Moon's mass is only 1.2% of Earth's!? That's because the Moon's average density is only 3.3 g/cm^3 compared to 5.5 g/cm^3 for Earth.
For more on that see answer(s) to Are there any known asteroids with average density similar to that of Earth's?
Visual cues are deceiving, these may help. Note that the larger beaker with the red fluid is filled to 600 ml, and the smaller one with blue fluid is only 60 ml, it looks like it's double in size but it's roughly 10x larger in volume!
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 1,083,206,916,845.7535 km³ (one trillion eighty-three billion bla-bla-bla cubic kilometers)
• The volume of Moon is 21,952,706,175.030006 km³ (twenty-one billion nine hundred and fifty-two million bla-bla-bla cubic kilometers, which is approximately twenty-two billion cubic kilometers)
Since one trillion is one thousand billion, you don't even need a calculator to understand that one trillion is roughly 50 times bigger than 21 billion, and one fiftieth (1/50) is exactly 2%.
Here is a picture of Earth and Moon shown as balls lying close to each other. You can use a ruler and see that the picture is true to life, the diameter of the smaller ball is really 27.3% (about 1/4) of the diameter of the bigger one: