Density is the measurement of the amount of mass per unit of volume. In order to calculate density, you need to know the mass and volume of the item. The mass is usually the easy part while volume can be tricky. Simple shaped objects are usually given in homework problems such as using a cube, brick or sphere. The formula for density is:

density = mass/volume

This example problem shows the steps needed to calculate the density of an object and a liquid when given the mass and volume.

**Question 1:** What is the density of a cube of sugar weighing 11.2 grams measuring 2 cm on a side?

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

Mass = 11.2 grams

Volume = cube with 2 cm sides.

Volume of a cube = (length of side)^{3}

Volume = (2 cm)^{3}

Volume = 8 cm^{3}

**Step 2: Plug your variables into the density formula.**

density = mass/volume

density = 11.2 grams/8 cm^{3}

density = 1.4 grams/cm^{3}

**Answer 1:** The sugar cube has a density of 1.4 grams/cm^{3}.

**Question 2:** A solution of water and salt contains 25 grams of salt in 250 mL of water. What is the density of the salt water? (Use density of water = 1 g/mL)

**Step 1: Find the mass and volume of the salt water.**

This time, there are two masses. The mass of the salt and the mass of the water are both needed to find the mass of the salt water. The mass of the salt is given, but the only the volume of water is given. We've also been given the density of water, so we can calculate the mass of the water.

density_{water} = mass_{water}/volume_{water}

solve for mass_{water},

mass_{water} = density_{water}·volume_{water}

mass_{water} = 1 g/mL · 250 mL

mass_{water} = 250 grams

Now we have enough to find the mass of the salt water.

mass_{total} = mass_{salt} + mass_{water}

mass_{total} = 25 g + 250 g

mass_{total} = 275 g

Volume of the salt water is 250 mL.

**Step 2: Plug your values into the density formula.**

density = mass/volume

density = 275 g/250 mL

density = 1.1 g/mL

**Answer 2:** The salt water has a density of 1.1 grams/mL.

### Finding Volume by Displacement

If you're given a regular solid object, you can measure its dimensions and calculate its volume. Unfortunately, the volume of few objects in the real world can be measured this easily! Sometimes you need to calculate volume by displacement.

How do you measure displacement? Say you have a metal toy soldier. You can tell it is heavy enough to sink in water, but you can't use a ruler to measure its dimensions. To measure the toy's volume, fill a graduated cylinder about half way with water. Record the volume. Add the toy. Make sure to displace any air bubbles that may stick to it. 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 (dry) toy and then calculate density.

### Tips for Density Calculations

In some cases, the mass will be given to you. If not, you'll need to obtain it yourself by weighing the object. When obtaining mass, be aware of how accurate and precise the measurement will be. The same goes for measuring volume. Obviously, you'll get a more precise measurement using a graduated cylinder than using a beaker, however, you may not need such a close measurement. The significant figures reported in the density calculation are those of your *least precise measurement*. So, if your mass is 22 kg, reporting a volume measurement to the nearest microliter is unnecessary.

Another important concept to keep in mind is whether your answer makes sense. If an object seems heavy for its size, it should have a high density value. How high? Keep in mind the density of water is about 1 g/cm³. Objects less dense than this float in water, while those that are more dense sink in water. If an object sinks in water, your density value better be greater than 1!

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