<blockquote>
<p>...despite having more than a quarter the 2-dimensional size of Earth.</p>
</blockquote>
<p>I think herein lies the problem; diameter is a 1-dimensional measurement, it's units are distance.</p>
<p>Let's rewrite 27.3% as 0.273. If that's the ratio of diameters, then the ratio of 2-dimensional <em>areas</em> should be (0.273)<sup>2</sup> and the ratio of the volumes should be (0.273)<sup>3</sup>. Those numbers are 0.0745 and 0.0203 respectively.</p>
<p>So the next question is why with a volume of 2% of Earth that <a href="https://en.wikipedia.org/wiki/Moon" rel="nofollow noreferrer">The Moon's mass is only 1.2% of Earth's</a>!?  That's because the Moon's average density is only 3.3 g/cm^3 compared to 5.5 g/cm^3 for Earth.</p>
<p>For more on that see answer(s) to <a href="https://astronomy.stackexchange.com/q/27930/7982">Are there any known asteroids with average density similar to that of Earth&#39;s?</a></p>
<hr />
<p>Visual cues are deceiving, these may help. Note that the larger beaker with the pale green fluid is filled to 600 ml, and the smaller one with red fluid is only 60 ml, it looks like it's double in size but it's roughly 10x larger in volume!</p>
<p><a href="https://i.sstatic.net/FwaPH.jpg" rel="nofollow noreferrer"><img src="https://i.sstatic.net/FwaPH.jpg" alt="large and small beakers" /></a></p>
<p>Sources: <strong>above:</strong> <a href="https://en.wikipedia.org/wiki/File:Beakers.jpg" rel="nofollow noreferrer">https://en.wikipedia.org/wiki/File:Beakers.jpg</a> and <strong>below:</strong> <a href="https://astronomy.stackexchange.com/q/16704/7982">Why does the Moon appear gray when passing between the Sun and the Earth?</a></p>
<p><a href="https://i.sstatic.net/FNXzZ.jpg" rel="nofollow noreferrer"><img src="https://i.sstatic.net/FNXzZ.jpg" alt="large and small astronomical bodies" /></a></p>

CC BY-SA 4.0
2020-07-17T08:19:01.310Z
@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: https://en.wikipedia.org/wiki/File:Beakers.jpg
uhoh
CC BY-SA 4.0
2020-07-17T06:23:52.033Z
2024-09-30T22:47:51.327Z
2024-09-30T22:47:51.327Z
uhoh
<p>It is all just geometry and mathematics.<br/>
The volume of a sphere is calculated according to this formula:</p>
<blockquote>
<p><strong>Volume = <span class="math-container">$(4/3) \times \pi \times r^3$</span></strong></p>
</blockquote>
<p>where <span class="math-container">$\pi$</span> = ‎3.14159..., and <span class="math-container">$r$</span> is the radius of the sphere.</p>
<p>The <strong>Earth</strong> radius is <strong>6,371 km</strong>.<br/>
The <strong>Moon</strong> radius is <strong>1,737 km</strong>.</p>
<p>We put the numbers into the formula and we get:<br/></p>
<p>• The <strong>volume of Earth</strong> is <strong>1,083,206,916,845</strong>.7535 km³ (one trillion eighty-three billion bla-bla-bla cubic kilometers)<br/></p>
<p>• The <strong>volume of Moon</strong> is <strong>21,952,706,175</strong>.030006 km³ (twenty-one billion nine hundred and fifty-two million bla-bla-bla cubic kilometers, which is approximately twenty-two billion cubic kilometers)</p>
<p>Since one trillion is one thousand billion, you don't even need a calculator to understand that <em>one trillion</em> is roughly 50 times bigger than <em>21 billion</em>, and one fiftieth (1/50) is exactly <strong>2%</strong>.</p>
<p>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:</p>
<p><a href="https://i.sstatic.net/J5szs.jpg" rel="nofollow noreferrer"><img src="https://i.sstatic.net/J5szs.jpg" alt="enter image description here" /></a></p>

CC BY-SA 4.0
2020-07-17T09:08:39.897Z
My question is concerning the volume despite the diameter, not the diameter despite the volume. But thank you nonetheless.
Ioannes
CC BY-SA 4.0
2020-07-17T09:58:11.553Z
@Greenhorn - The volume of a sphere depends _only_ on its diameter/radius, nothing else.
Yellow Sky
CC BY-SA 4.0
2020-07-17T10:44:22.517Z
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.
Ioannes
CC BY-SA 4.0
2020-07-17T08:05:02.203Z
2020-07-17T08:25:54.063Z
2020-07-17T08:25:54.063Z
Yellow Sky
<p>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.</p>
<p>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.</p>
<p><a href="https://i.sstatic.net/76r6C.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/76r6C.png" alt="enter image description here" /></a></p>
<p>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.</p>
<p><a href="https://i.sstatic.net/bBUr9.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/bBUr9.png" alt="enter image description here" /></a></p>
<p>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.</p>

CC BY-SA 4.0
2023-09-12T07:23:20.133Z
2023-09-12T07:23:20.133Z
J Demi
<p>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?</p>

CC BY-SA 4.0
2020-07-17T05:40:41.287Z
That's just geometry. $(0.273)^{3} \approx 0.02035$
PM 2Ring
CC BY-SA 4.0
2020-07-17T05:42:52.967Z
Look the volume of a sphere (close enough for comparison).
Fred
CC BY-SA 4.0
2020-07-17T05:57:14.913Z
@PM2Ring From google I get a result of 0.085. That would sound credible for the Moon.
Ioannes
CC BY-SA 4.0
2020-07-17T06:26:58.743Z
I dont know what you mean. Where does that 0.085 come from? BTW, the radius is a 1 dimensional measure of size, not 2 dimensional. From Google, I get 1,737.1 km & 6,371 km for the radii of the Moon & the Earth. Their ratio is ~= 0.2727, (which is slightly smaller than the value given in your question), so the ratio of their volumes is the cube of that, ~= 0.02027
PM 2Ring
CC BY-SA 4.0
2020-07-17T06:31:02.787Z
@PM2Ring My value is rounded up (you could've guessed this) and also depends on latitude and mountains. Google "volume of a sphere" and enter 0.273 into the calculator.
Ioannes
CC BY-SA 4.0
2020-07-17T07:08:11.967Z
That calculator is designed so that you enter _radius or diameter_ of a sphere in it, but **not** the _ratio_ or two radii/diameters!
Yellow Sky
CC BY-SA 4.0
2020-07-17T08:55:59.643Z
Yes, I realise your 0.273 is rounded up. If you put 1 as the radius into the sphere volume calculator, you'll get V≈4.19. And 0.085/4.19≈0.0203
PM 2Ring
CC BY-SA 4.0
2020-07-17T08:59:01.803Z
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 $k^3$.
PM 2Ring
<the-moon><size>
Why is the Moon's volume so small compared to the Earth's?
Ioannes
# Why is the Moon's volume so small compared to the Earth's?

(Asked by: username_0 on 2020-07-17)

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?

**Tags:** the-moon, size

> **Comments:**
> **username_1**: That's just geometry. $(0.273)^{3} \approx 0.02035$  
> **username_2**: Look the volume of a sphere (close enough for comparison).  
> **username_0**: @username_1 From google I get a result of 0.085. That would sound credible for the Moon.  
> **username_1**: I dont know what you mean. Where does that 0.085 come from? BTW, the radius is a 1 dimensional measure of size, not 2 dimensional. From Google, I get 1,737.1 km & 6,371 km for the radii of the Moon & the Earth. Their ratio is ~= 0.2727, (which is slightly smaller than the value given in your question), so the ratio of their volumes is the cube of that, ~= 0.02027  
> **username_0**: @username_1 My value is rounded up (you could've guessed this) and also depends on latitude and mountains. Google "volume of a sphere" and enter 0.273 into the calculator.  
> **username_3**: That calculator is designed so that you enter _radius or diameter_ of a sphere in it, but **not** the _ratio_ or two radii/diameters!  
> **username_1**: Yes, I realise your 0.273 is rounded up. If you put 1 as the radius into the sphere volume calculator, you'll get V≈4.19. And 0.085/4.19≈0.0203  
> **username_1**: 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 $k^3$.  

---

## 3 answers

### Answer by username_4 on 2020-07-17. Score: 3 | Accepted answer

> ...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](https://en.wikipedia.org/wiki/Moon)!? 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?](https://astronomy.stackexchange.com/q/27930/7982)

---

Visual cues are deceiving, these may help. Note that the larger beaker with the pale green fluid is filled to 600 ml, and the smaller one with red fluid is only 60 ml, it looks like it's double in size but it's roughly 10x larger in volume!

[![large and small beakers](https://i.sstatic.net/FwaPH.jpg)](https://i.sstatic.net/FwaPH.jpg)

Sources: **above:** <https://en.wikipedia.org/wiki/File:Beakers.jpg> and **below:** [Why does the Moon appear gray when passing between the Sun and the Earth?](https://astronomy.stackexchange.com/q/16704/7982)

[![large and small astronomical bodies](https://i.sstatic.net/FNXzZ.jpg)](https://i.sstatic.net/FNXzZ.jpg)

> **Comments:**
> **username_4**: @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: https://en.wikipedia.org/wiki/File:Beakers.jpg  

---

### Answer by username_3 on 2020-07-17. Score: 3

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:

[![enter image description here](https://i.sstatic.net/J5szs.jpg)](https://i.sstatic.net/J5szs.jpg)

> **Comments:**
> **username_0**: My question is concerning the volume despite the diameter, not the diameter despite the volume. But thank you nonetheless.  
> **username_3**: @Greenhorn - The volume of a sphere depends _only_ on its diameter/radius, nothing else.  
> **username_0**: 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.  

---

### Answer by username_5 on 2023-09-12. Score: 1

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.

[![enter image description here](https://i.sstatic.net/76r6C.png)](https://i.sstatic.net/76r6C.png)

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.

[![enter image description here](https://i.sstatic.net/bBUr9.png)](https://i.sstatic.net/bBUr9.png)

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.


---

