# Math Help - Surface to Volume Ratio

1. ## Surface to Volume Ratio

I calculated the Surface to Volume Ratio of a 12 inch cube as follows.

Volume 12x12x12=1728
Surface Area 12x12x6=864
Ratio 864/1728=1:2

I then calculated for the same cube but measured in centimetres (30)

Volume 30x30x30=27000
Surface Area 30x30x6=5400
Ratio 5400/27000=1:5

Could somebody please tell me why I get a different value for the ratio?
What am I doing wrong?

2. Originally Posted by Calleva
I calculated the Surface to Volume Ratio of a 12 inch cube as follows.

Volume 12x12x12=1728
Surface Area 12x12x6=864
Ratio 864/1728=1:2

I then calculated for the same cube but measured in centimetres (30)

should be 30.48 ...

Volume 30x30x30=27000
Surface Area 30x30x6=5400
Ratio 5400/27000=1:5

Could somebody please tell me why I get a different value for the ratio?
What am I doing wrong?
nothing wrong ... different ratio because

inch:cm = 1:2.54

3. ## Thanks

I am still confused.
Does this mean that the ratio for a given cube varies depending upon which units you use to measure it?

4. Originally Posted by Calleva
I am still confused.
Does this mean that the ratio for a given cube varies depending upon which units you use to measure it?
correct, consider a cube with sides equal to 1 ft ...

surface area to volume would be 6 square feet :1 cubic ft ... 6:1

using inches ... 864 square inches : 1728 cubic inches ... 1:2

units matter.

5. This ratio is not a "dimensionless number": volume is in units of length cubed. Area is in units of length squared. The ratio is $\frac{volume}{area}= \frac{length^3}{length^2}= length$. If you calculate the volume and area in meters, the ratio will have units of meters. If you calculate the volume and area in feet, the ration will have units of feet. Since they are in different unit systems, the numbers will not be the same- one meter is not the same as one foot.

6. Got it.
Thanks again.