# Why is the Moon's volume so small compared to the Earth's?

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?

• That's just geometry. $(0.273)^{3} \approx 0.02035$ Jul 17, 2020 at 5:40
• Look the volume of a sphere (close enough for comparison).
– Fred
Jul 17, 2020 at 5:42
• @PM2Ring From google I get a result of 0.085. That would sound credible for the Moon. Jul 17, 2020 at 5:57
• That calculator is designed so that you enter radius or diameter of a sphere in it, but not the ratio or two radii/diameters! Jul 17, 2020 at 7:08
• But you don't need to worry about the formula for the volume of a sphere. If you have two 3D objects of identical shape, and the ratio of their linear sizes is $k$, then the ratio of their volumes is $k^3$. Jul 17, 2020 at 8:59

...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!

• @Greenhorn it's not intuitive, our brains don't naturally think that way I know. But it's really true! If you can find small and large drinking glasses or glass beakers of the same shape but different sizes, try pouring one into the other. If the large one is twice the size of the small one, you'll have to fill and empty the smaller one eight times to fill the larger one. 60 ml vs 600 ml: en.wikipedia.org/wiki/File:Beakers.jpg
– uhoh
Jul 17, 2020 at 8:19
• This might be entirely off-topic, but isn't the larger beaker filled with a pale greenish yellow liquid and the smaller beaker filled with a red liquid? Or are my eyes playing tricks on me?!
– user26067
Jul 17, 2020 at 12:58
• My eyes are also fooling me, the stuff in the large beaker looks pale green and the stuff in the small beaker looks bright red. Jul 17, 2020 at 14:04

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:

• My question is concerning the volume despite the diameter, not the diameter despite the volume. But thank you nonetheless. Jul 17, 2020 at 9:08
• @Greenhorn - The volume of a sphere depends only on its diameter/radius, nothing else. Jul 17, 2020 at 9:58
• I know. You seem to make the assumption that it's the diameter I'm wondering about. I'm wondering about the volume, not the 1-dimensional size. Jul 17, 2020 at 10:44

Smh. Get something to draw with. Draw a circle. Draw 3 more the same size in a line. Each new circle should be touching the previous one. Now draw a big circle around the first four with the left most edge of the big circle touching the left most side of first small circle and the right most edge of the big circle touching the right most side of the 4th small circle.

Our small circles have a diameter that is 25% of the diameter of the large circle. It's not 27.3%, but its lose enough for explaining.

You can easily see our small circles take up a LOT less of an area than the big one. Now go ahead and fill that large circle with the small ones.

Fit a lot in didn't you? Imagine this in 3 dimensions. Since we're talking about how a sphere with a diameter thats 1/4 less than a bigger sphere can only have a volume that's only 2% of the bigger spheres volume, let's not forget about all the spaces between our spheres, those take up volume too.