Density: compare equal amounts of space

Heavier is not always denser

Imagine comparing two sample blocks. One has more mass, but it also takes up more space. Mass alone cannot tell us which is denser. Density compares mass with volume. In this lesson, we use grams for mass and cubic centimeters for volume, then divide mass by volume.

Read the first sample

Sample A has mass twenty-four grams and volume eight cubic centimeters. Twenty-four divided by eight is three. Its density is three grams per cubic centimeter. This is the sample's average mass per unit of volume, so keep both parts of the unit in your answer.

A larger sample can match it

Sample B has forty-eight grams of mass and sixteen cubic centimeters of volume. Divide forty-eight by sixteen and you also get three grams per cubic centimeter. B has twice the mass and twice the volume. It is a larger sample, but not a denser one in this example.

Use density to find mass

If you know density and volume, multiply them to find mass. A sample with density four grams per cubic centimeter and volume six cubic centimeters has mass twenty-four grams. Think of four grams for each of six cubic centimeters. The units describe what the multiplication is doing.

Pause: find a new sample's density

Pause for a new sample. Its mass is thirty grams and its volume is ten cubic centimeters. Calculate its density and include the units. Then compare it with samples A and B. Do not choose a denser sample simply by looking for the largest mass.

Compare the calculated ratios

Thirty divided by ten is three grams per cubic centimeter. This new sample has the same stated density as A and B, even though the masses and volumes differ. To compare density, compare the ratios in matching units. A giant label saying heavy is not enough evidence.

A ratio can stay unchanged

Fun fact: doubling both mass and volume leaves their ratio unchanged. That is exactly what happens from A to B in our diagram. For portions of the same uniform material under the same conditions, sample size alone does not change density. Material and conditions still matter.

Keep the quantities distinct

Continue to the density worksheet. List the quantities you know before choosing a calculation. Divide mass by volume for density, multiply density by volume for mass, or divide mass by density for volume. Keep your units visible and explain why a bigger sample need not be denser.