Finding the Density of a Solid

Density

Remember that density is a measure of the amount of stuff packed into a space. Different liquids and different solutions will have different densities and determining the density of a solution can help identify the solution.

Mathematically, we use the formula \(d=\frac{mass}{volume}\). This means that to find the density of something, we need to know the mass and volume. There are several ways to do this for a solid.

Finding the Density of a Regular Solid

Finding the density of a regular solid is very straightforward. Mass is measured on a balance and then volume is found by measuring the the solid and doing simple geometric math.

Cubes and Rectangular Prisms

Cylinders

Finding the Density of Irregular Solids

An irregular solid is one whose shape is not a simple geometric figure. This could be anything ranging from a slightly irregular block (where the corners aren’t quite square) to a random unsightly chunk.

Again, mass is easy. We simply put the solid on a balance.

Volume is now the challenge. In such a case, we find the volume using Archimedes Principle. The idea that a solid will displace a volume of water equal to its own volume.

If you aren’t familiar with the Archimedes Principle, the VERY short version of the story is that Archimedes was charged by the king to determine if the man who had made his new crown had cheated him by mixing the gold he had been given with another metal. The only way to identify pure gold at the time was to measure the density. However, the crown, being “crown-shaped” did not have an obvious volume. While pondering how to determine the volume of the crown, Archimedes went to the public baths. When he lowered himself into the tub, a large amount of water splashed over the side and Archimedes realized he could measure the volume of the crown by measuring the water displaced. He was so excited that he jumped up and ran through the town (naked) crying Eureka (I’ve found it).

Using the Archimedes Principle is simple. We find a graduated cylinder that has a wider diameter than the object and fill it part way with water. Carefully measuring the volume. Then we place the object into the cylinder so that it is completely submerged. As a result of this, the water will rise up the cylinder. We can then read the new volume. The volume of the object is simple the difference between the two measured volumes:

\(volume~of~object = volume~with~object - volume~without~object\)

So the density can be found this way:

\(density = \frac{mass}{(volume~with~object - volume~without~object)}\)