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

1 Answer
Jul 11, 2016

Answer:

#"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"#.

http://www.savannahfreight.com/blog/2015/10/08/What-is-a-cubic-meter-How-much-to-ship-it.aspx

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)|)))#