Density Worked Example Problem

Density is a measure of how much matter is in a space. It is expressed in units of mass per volume, such as g/cm³ or kg/L. This is a worked example of how to calculate the density when given the volume and mass of a substance.

Sample Density Problem

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An Introduction to Density: Definition and Calculation

By Andrew Zimmerman Jones

A brick of salt measuring 10.0 cm x 10.0 cm x 2.0 cm weighs 433 grams. What is its density?

Solution:

Density is the amount of mass per unit volume, or:
D = M/V
Density = Mass/Volume

Step 1: Calculate Volume

In this example, you are given the dimensions of the object, so you have to calculate the volume. The formula for volume depends on the shape of the object, but it's a simple calculation for a box:

Volume = length x width x thickness
Volume = 10.0 cm x 10.0 cm x 2.0 cm
Volume = 200.0 cm³

Step 2: Determine Density

Now you have the mass and the volume, which is all the information you need to calculate density.

Density = Mass/Volume
Density = 433 g/200.0 cm³
Density = 2.165 g/cm³

Answer:

The density of the salt brick is 2.165 g/cm³.

A Note About Significant Figures

In this example, the length and mass measurements all had 3 significant figures. So, the answer for density should also be reported using this number of significant figures. You'll have to decide whether to truncate the value to read 2.16 or whether to round it up to 2.17.