Density is the relationship that exists between the mass of a substance or a body and its volume *(fields of physics and chemistry)* , that is, it is the measurement of mass by the amount of volume, and its formula is:

Density= mass/volume M/V

- Mass
*is the amount of matter that makes up a body.* *Volume is the space occupied by a body*.

*“We are talking about an intrinsic property, since this does not depend on the amount of substance that is considered.”*

## Let’s put it into practice

Question: What is the density of a sugar cube that weighs 11.2 grams and measures 2 cm on a side?

Step 1: Find the mass and volume of the sugar cube.

Mass = 11.2 grams Volume = cube with sides of 2 cm.

Volume of a cube = (length of side) 3

Volume = (2 cm) 3

Volume = 8 cm3

Step 2 – Insert your variables into the density formula.

density = mass / volume

density = 11.2 grams / 8 cm3

density = 1.4 grams / cm3

Answer: The sugar cube has a density of 1.4 grams/cm3.

## Tips for removing calculations

Solving this equation will, in some cases, deliver the mass. Otherwise, you yourself must obtain it thinking about the object. When having the mass, keep in mind how accurate the measurement will be. The same goes for volume, clearly the measurement would be more accurate with a graduated cylinder than with a beaker, however you may not need as accurate a measurement.

Another important point to keep in mind to know if your answer makes sense. When an object seems too heavy for its size, it should have a high density value. How much? Thinking that the density of water is about 1 g/cm³. Objects less dense than this would be sinking in the water. So, if an object sinks in water, its density value should mark you as greater than 1!

## volume per displacement

If you are given a regular solid object, its dimensions can be measured and thus calculate its volume, however, the volume of few objects in the real world cannot be measured so easily, sometimes it is necessary to calculate the volume by displacement.

- By Archimedes’ Principle it is known that the mass of the object is obtained by multiplying its volume by the density of the fluid. If the density of the object is less than that of the displaced liquid, the object floats; if it is greater, it sinks.
- Displacement can be used to measure the volume of a solid object, even if its shape is not regular.

How is displacement measured? Let’s say you have a metal toy soldier. You can tell it’s heavy enough to sink in water, but you can’t use a ruler to measure its dimensions. To measure the volume of the toy, fill a graduated cylinder halfway with water. Record the volume. Add the toy. Be sure to displace any air bubbles that may stick. Record the new volume measurement. The volume of the toy soldier is the final volume minus the initial volume. You can measure the mass of the toy (dry) and then calculate the density.