Question

How would you relate the volume of a container (in cm3) to the volume of liquid it contains (in mL)?

Answer 1

Both the `cm^3` and the `mL` are units of volume. It is a fact that there are `10^3*L` in a `m^3`. How does this help us?

Explanation:

`1*mL=1xx10^-3L`

But `1*cm^3` `=` `(1xx10^-2m)^3` `=` `1xx10^-6*m^3`

`=` `10^-6*m^3*L^-1xx10^3*Lm^-3` `=` `10^-3*L` `=` `1*mL` as required.

Sometimes, especially in English (i.e. UK) texts, you will find the `L` quoted as `1*dm^3`, i.e `"deci ="1/10`.

`1*dm^3` `=` `(1xx10^-1m)^3` `=` `1/10^3m^3` `=` `1*L` as required.