A scientist has three cubes of different materials. Each cube has a volume of 125 cubic centimetres. She weighs each cube to find its mass. And her results are recorded in the table shown. Which material has the highest density?
Taking a look at this table, we see that, in the first column, the material is listed, in the second column, the material volume, and in the third column, the material mass. We want to know which of these materials has the highest density. Let’s start off by recalling just what density is. This term, often represented using the Greek letter 𝜌, is equal to the mass of an object divided by the space that object takes up, its volume. In our table, we have both mass and volume recorded for these three different materials.
Basically, there are two ways we could go about answering this question of solving for the material with the highest density. Since density is equal to mass divided by volume and we have the mass and volume for each of these three materials, we could go through one by one and calculate the density of each. Then, answering our question would just be a matter of picking which density is highest.
That’s one way to do it. But there’s another way to answer this question. And that is to use the fact that we’re told that each of these cubes has a volume of 125 cubic centimetres. Now, it doesn’t particularly matter that the volume is that number, 125 cubic centimetres. But what’s important is that all the volumes are the same. This means that when it comes to calculating density because the volumes of these three materials are all the same, that term, volume, won’t play a role in determining which density is highest and lowest.
For the purposes of our question then, we can ignore volume because all the materials have the same one. That means that everything comes down to mass. Whichever material has the greatest mass will also have the greatest density. While this isn’t usually the case, it is true in our situation just because all the volumes of the materials are the same.
So to find the material with the highest density, we just need to find the material with the highest mass. And going down the list, we see that 1.12 kilograms is the highest measure mass value. And the material corresponding to that mass is copper. And this then is our choice for the material with the highest density. Because the volumes of all three of our candidate materials happen to be the same, we were able to take a bit of a shortcut in finding which one has the highest density.