Scale by Volume of Object in Blender

Question

I have two skulls like so:

Using the 3D print addon toolbox, I know the volumes of each:

747735056401 for the larger one
569718590290 For the smaller one

I'd like to scale the smaller one to be the same volume as the larger one.   Not being a math wiz, I simply did:  747735056401/569718590290= 1.312464,  so I hit S and typed in 1.312464.
But, I didn't even realize that would just scale the x,y,z dimensions and all of a sudden my new volume had gone way up to 12880819961337.   Way larger than intended.
Does anyone either know (through a Blender command, or through better math understanding) how I could scale the volume of one to be the same as the other?

Rich Sedman · Accepted Answer

The volume is proportional to the cube of the scale. For example, doubling all of the dimensions would result in a volume that is 2x2x2 = 8 times the volume.
Therefore, in order to scale the volume by 1.312464 you have to scale each dimension by the cube root of 1.312464. ie, approximately 1.0948678.

Scale by Volume of Object in Blender

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