Question

How many `cm^3` in a `10*m^3` volume?

Answer 1

`1` `cm^3` `=` `1xx(10^-2*m)^3`. There are thus `10^7` `cm^3` in a `10` `m^3` volume.

Explanation:

The `"centi"` prefix means `10^-2`.

So `1` `cm^3` `=` `(1xx10^-2*m)^3` `=` `(1xx10^-2*mxx1xx10^-2*mxx1xx10^-2*m)` `=` `1xx10^-6*m^3`.

Thus there are 1 million `cm^3` in a cubic metre. Do you agree? All I have done is expanded the prefix `"centi"` using the cubic exponent. Since, there are `1` `million` `cm^3` in a cubic metre, there are `10xx10^7` `cm^3` in a `10` `m^3` volume.

The conversion factor is `10^6` `cm^3m^-3`