Hi Welcome to MooMooMath. Today we are going to talk about changing measurements when you are going from one dimension to two dimensions to three dimensions. What you will do is take your linear measurement which is one dimensional and compare it to an area. You would take your unit and to find your unit ratio in area you would square that unit. Let’s say you have a linear measurement and you are changing it to a volume measurement you would take that unit and cube it because volume is three dimensional. So you always go back to your original linear measurement and square it for area and cube it for volume. So let’s look at an example of what I’m talking about. Let’s say you have a rug that is one yard by one yard or one square yard which equals three feet on one side. My linear measure would be three. So if I have one square yard how many square feet would that be? So I would take three squared or nine so it would be 9 square feet. Let’s say I have this and I’m going into three dimension and I have a cube that is one yard on each side which is 3 feet. What would be the volume of that? One cubic yard is (remember the linear measure is one to three) so we will cube three to 27 so one cubic yard is 27 cubic feet. I have drawn a rendition here if you have a Rubik’s cube you have 27 squares on it so you have (counts to 9) have nine in each row and three rows which makes 27 little cubes inside the rubrics cube. So that is how you convert the ratio of measurements.

Area to volume-Linear measurements

Examples of changing measurements from linear measure to area to volume.

Example 1. In example 1 above you have a rug that is 3 feet on one side. Therefore you have an area of 9 square feet and a volume of 27 cubic feet.

Example 2 In example 2 you have an object that has a linear measure of 5 inches. The area of this object would be 25 square inches and a volume of 125 cubic inches,

How to convert from Linear measure,to Area measure, to Volume Measure

Linear measurements are always one dimensional, area measurements are two dimensional, and volume are three dimensional. The chart below summarizes changing measurements from linear measurements, and volume measurements.