Using the density formula to find mass or volume written by: pesasukko Using the density formula to find mass or volume

Your physics or chemistry teacher probably taught you that density of any substance is its mass per unit volume. They probably also showed you a formula for calculating density. If you were a diligent student, you would have also used the formula to find the mass and volume. However, in case you weren’t paying attention in class that day, you can review how to do that here. mass formula  

Let’s start by reviewing the formula to calculate density. If you know the mass and volume of a substance, you can calculate its density using this formula:
Density = Mass/Volume

For example, if 3kg of iron occupies a space 20m3, using the formula above, the density of iron would be:
Density = Mass/volume
= 3kg/20m3
=0.15kg/m3

Now it is also possible to tweak this formula to calculate either the mass or the volume.This can be done using knowledge of simple mathematical principles. If you can’t remember how your teacher did it, study the equations below carefully until you can do it yourself. Suppose you knew both the density of a substance and its volume but wanted to find its mass. Starting from the formula for density which you already know:

Density = Mass/Volume

Multiply both sides of the equation by Volume.
Density * Volume = Mass/Volume * Volume
Volume on the right-hand side of the equation cancels out. You are left with:
Density * Volume = Mass

You can flip the formula around to get:
Mass = Density * Volume

Using the same example as above, we know the density of iron is 0.15kg/m3 and its volume is 20m3. Now to find the mass,
Mass = Density * Volume
= 0.15kg/m3 * 20m3
= 3kg

Easy, right? If, on the other hand, you knew the mass and density of a substance but wanted to find its volume, remember our original formula:
Density = Mass/Volume

Multiply both sides of the equation by 1/Mass
Density * 1/Mass = Mass/Volume * 1/Mass
Mass on the right-hand side of the equation cancels out. You are left with:
Density/Mass = 1/Volume

You can take the inverse of this equation (flip both sides upside down). Your equation would become:
Mass/Density = Volume
Therefore, Volume = Mass/Density

Still using the same example, if you knew 3kg of iron has a density of 0.15kg/m3 but wanted to find its volume. Using your newly worked out formula:
Volume = Mass/Density
= 3kg/0.15kg/m3
=20m3

This tallies with our initial information. In general, it is possible to tweak a formula where one variable is unknown in order to find that variable. This is called changing the subject of the formula. Study the way this has been done with this example until you can do this on your own. Follow the steps carefully. If you have trouble with any of the steps above, you should brush up on your knowledge of changing the subject of the formula.Remember, the best way to learn is through practice.

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