<p>The surface area of a sphere is $A=4\pi r^2$ and the volume is $V=\frac 4 3 \pi r^3$.</p>

<p>Now the ratio $a = \frac {A_{saturn}} {A_{earth}} = (\frac {r_{saturn}} {r_{earth}})^2$</p>

<p>and the volume ratio is $b = \frac {V_{saturn}} {V_{earth}} = (\frac {r_{saturn}} {r_{earth}})^3$</p>

<p>The resulting ratio is $a = b ^{\frac 2 3}$.</p>

<p>User @Alex added that in your example, $764^{\frac 2 3}\approx83.6$, which I'd neglected to mention.  Thank's @Alex.</p>

<p>And clearly that won't be equal to unless the two planets had the same radius.</p>

CC BY-SA 3.0
2017-05-09T13:29:59.367Z
You could add that for this particular case $764^{2/3} = 83.6$...
Alex
CC BY-SA 3.0
2017-05-07T19:21:42.367Z
2017-05-09T14:40:07.187Z
2017-05-09T14:40:07.187Z
StephenG - Help Ukraine
<p>If Saturn is 83x bigger that Earth by surface area why isn't the volume also 83x bigger than earth by volume? Is there a geometric or astronomical reason?</p>

CC BY-SA 3.0
2017-05-07T18:43:29.993Z
Surface area is proportional to the square of the radius.    Volume, the cube of the radius.   Saturn's radius is about 9 times Earth's.   Each extra dimension requires the additional multiple of that 9 times the size.   Surface area is 2 dimensions.   Volume is 3 dimensions.
userLTK
CC BY-SA 3.0
2017-05-07T19:57:55.233Z
Please put answers in answers, not in comments
James K
CC BY-SA 3.0
2017-05-09T13:39:47.973Z
I'm voting to close this question as off-topic because it's very basic geometry and not at all specific to astronomy.
Warrick
<saturn><space-geometry>
Why is the volume of Saturn is 764 times bigger than Earth, but its surface area only 83 times bigger?
user16821
# Why is the volume of Saturn is 764 times bigger than Earth, but its surface area only 83 times bigger?

(Asked by: username_0 on 2017-05-07)

If Saturn is 83x bigger that Earth by surface area why isn't the volume also 83x bigger than earth by volume? Is there a geometric or astronomical reason?

**Tags:** saturn, space-geometry

> **Comments:**
> **username_1**: Surface area is proportional to the square of the radius.    Volume, the cube of the radius.   Saturn's radius is about 9 times Earth's.   Each extra dimension requires the additional multiple of that 9 times the size.   Surface area is 2 dimensions.   Volume is 3 dimensions.  
> **username_2**: Please put answers in answers, not in comments  
> **username_3**: I'm voting to close this question as off-topic because it's very basic geometry and not at all specific to astronomy.  

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## 1 answers

### Answer by username_4 on 2017-05-07. Score: 2

The surface area of a sphere is $A=4\pi r^2$ and the volume is $V=\frac 4 3 \pi r^3$.

Now the ratio $a = \frac {A\_{saturn}} {A\_{earth}} = (\frac {r\_{saturn}} {r\_{earth}})^2$

and the volume ratio is $b = \frac {V\_{saturn}} {V\_{earth}} = (\frac {r\_{saturn}} {r\_{earth}})^3$

The resulting ratio is $a = b ^{\frac 2 3}$.

User @username_5 added that in your example, $764^{\frac 2 3}\approx83.6$, which I'd neglected to mention. Thank's @username_5.

And clearly that won't be equal to unless the two planets had the same radius.

> **Comments:**
> **username_5**: You could add that for this particular case $764^{2/3} = 83.6$...  

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