Example of Using Unit Conversions for Volume

Narrator: Welcome in this video we’re going to show an example of using unit conversions for volume. [a cube split into 9 cubes] Let’s say this represents a cubic yard of mulch. Mulch is decaying plant material that can be used to enrich the soil in a garden or a flowerbed. So this is one yard by one yard by one yard. It’s one cubic yard so one yard cubed.

In this story the place that sells mulch charges 20 dollars per one cubic yard. How much is it per cubic meter? So what is the cost per meter cubed? So in order to do this problem I need to find the conversion factor between yards cubed and meters cubed. So one yard is equal to zero point 9144 meters. It’s just a little bit smaller than a full meter. So if one yard is equal to zero point 9144 meters then one square yard so one yard square is equal to zero point 9144 meters squared. Cuz we get one yard squared by squaring one yard. One times one is one, yard times yard is yard squared.

Similarly if we make this a cube, one cubic yard which is now one yard height, we can find the number of meters cubed of this one cubic yard by cubing our meters. So one yard all cubed equals zero point 9144 meters all cubed. So one cubic yard equals, now we put into our calculator this number and cube it to find the meters cubed. [on calculator 0.764554857984] So point 9144 cubed equals zero point 76, I’m going to round this to a 5, zero point 765 meters cubed. Zero point 765 meters cubed. Now we can use this conversion factor to help us solve our problem.

So first of all we need to figure out what we want our units to be at the end of our equation. Well we want to know how much it costs per meter cubed. So we want in this case we’re using dollars so we want dollars per meter cubed. This will tell us how much it costs for a meter cubed of mulch. Because we want dollars on top at the end we’re going to start with our dollars on top at the beginning so we’re going to start with 20 dollars which is equal to one cubic yard. So 20 dollars can buy one cubic yard. Now we need to convert from cubic yards to meters cubed to find out the cost in dollars for meters cubed. 

So now we multiply by a version of one in the form of our conversion factor and we’re going to want our yards cubed in the numerator so yards cubed in the numerator so that they can cancel each other out. Well our previous calculation found that one cubic yard is equal to zero point 765 meters cubed so now our yard cubed can cancel and we’re left with dollars in the numerator and meters cubed in the denominator. So now we can do our calculation so 20 divided one doesn’t change it. So we can just leave it at 20 then we multiply by the numerator of the next unit conversion which is just one which again doesn’t change our answer. Then we divide by the denominator. Divided by point 765 equals 26 point 14. [on calculator 26.143790849673203] So that means it costs 26 point 14 dollars per one meter cubed of the mulch. The key to this was figuring out what we wanted in the end. The units we wanted in the end and then putting our units at the beginning in the correct order in the numerator and the denominator to help us get those units at the end.

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