# Dimensional Analysis with volume?

1. Aug 28, 2011

### Titandwedebil

Can you work units cubed the same way you can work units that aren't cubed in dimensional analysis?

Like...does 1m3 equal 250cm3 like it would if they weren't cubed?

2. Aug 28, 2011

### Mute

I'm not sure where you're getting 1 m^3 = 250 cm^3, but here's how things work:

If you have 1 m^3 and you want to convert to cm cubed, you can use the fact that 1 m = 100 cm. Since 1 m^3 is really just (1 m)^3, I can write (1 m)^3 = (100 cm)^3. The power of 3 now has to distribute over both the unit and the number, so we get that

1 m^3 = 100^3 cm^3 = 10^6 cm^3.

The key point to take away is that a relation between units like 1 m = 100 cm is an equality, so you can always replace a unit with one of these equalities, and then distribute the powers over both the unit and the number, as done in this example here.