# How do you convert "m"^3 to "cm"^3?

Jul 11, 2016

${\text{1 m"^3 = 10^6"cm}}^{3}$

#### Explanation:

All you need to know here is the following conversion factor

$\textcolor{p u r p \le}{| \overline{\underline{\textcolor{w h i t e}{\frac{a}{a}} \textcolor{b l a c k}{\text{1 m" = 10^2"cm}} \textcolor{w h i t e}{\frac{a}{a}} |}}}$

Now, a cubic meter can be thought of as the volume of a cube with a side of $\text{1 m}$.

You can write the volume of the cube by raising the length of its side to the power of $3$

$\text{1 m"^3 = "1 m" xx "1m" xx "1 m}$

Notice that you can use the meter $\to$ centimeter conversion factor to rewrite this as

"1 m"^3 = overbrace(10^2"cm")^(color(blue)("= 1 m")) xx overbrace(10^2"cm")^(color(blue)("= 1 m")) xx overbrace(10^2"cm")^(color(blue)("= 1 m"))

You will thus have

"1 m"^3 = (10^2 xx 10^2 xx 10^2) ("cm" xx "cm" xx "cm")

which gets you

$\textcolor{g r e e n}{| \overline{\underline{\textcolor{w h i t e}{\frac{a}{a}} \textcolor{b l a c k}{{\text{1 m"^3 = 10^6"cm}}^{3}} \textcolor{w h i t e}{\frac{a}{a}} |}}}$