How to use metric conversion with volume?

Question

So this is the metric conversion - K h d b d c m I can't understand how you can convert metric squared units to volume squared units or vice versa. For example converting 3400 mm squared to ml squared, how should you proceed while using the metric conversion? So in a nutshell, can someone explain how one can convert volume to distance (that being said cm, m, km, dm, etc) WHILE using the metric conversion system?

Answer 1

Unit conversions only make sense when the type of unit is the same before and after.

If you have a length in feet, you'll need a length after the conversion. This can be measured in millimeters, furlongs, or parsecs.

If you have a volume before, you'll need a volume after. If you have a force before, you'll need a force after. Etc.

To get to your example: $3400$ $mm^2$ is an area. You can convert this to acres, square feet, etc.

But I've never seen, nor even imagined, what a square milliliter looks like. A milliliter is a unit of volume, which is equivalent to a length cubed. So a square milliliter has the dimensions of a length to the sixth power. These kinds of things don't exist in our universe, to my knowledge.

This is the same reason you can't convert a volume to a distance. The dimensions are different.