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

##### 1 Answer

#### Explanation:

All you need to know here is the following *conversion factor*

#color(purple)(|bar(ul(color(white)(a/a)color(black)("1 m" = 10^2"cm")color(white)(a/a)|)))#

Now, a *cubic meter* can be thought of as the volume of a cube with a side of

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

#"1 m"^3 = "1 m" xx "1m" xx "1 m"#

Notice that you can use the *meter* *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

#color(green)(|bar(ul(color(white)(a/a)color(black)("1 m"^3 = 10^6"cm"^3)color(white)(a/a)|)))#