Question

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

Answer 1

`"1 m"^3 = 10^6"cm"^3`

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 `"1 m"`.

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

`"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)|)))`