Calculating Density

Calculating Density

Middle School

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Learning Objectives

Key Vocabulary

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Density

The amount of matter in a given space, reflecting how closely packed particles are.

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Mass

The measure of the amount of matter that makes up an object, often measured in grams (g).

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Volume

The amount of three-dimensional space an object or substance occupies, measured in cm³ or mL.

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What Is Density?

High Density

• ​Particles are packed tightly together in a specific amount of space.

• ​​This means there is more mass, or 'stuff,' in the same volume.

• ​A bowling ball is a good example of an object with high density.

Low Density

• ​Particles are spread far apart in the same amount of space.

• ​​This means there is less mass, or 'stuff,' in the same volume.

• ​A volleyball is a good example of an object with low density.

Multiple Choice

Which of the following statements best describes density?

• How heavy an object is.

• The amount of space an object takes up.

• How closely packed the particles of matter are in a substance.

• The shape and texture of a substance.

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The Formula for Density

Multiple Choice

What is the density of a liquid that has a mass of 300 g and a volume of 30 mL?

• 10 g/mL

• 0.1 g/mL

• 330 g/mL

• 9000 g/mL

Finding Mass and Volume

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Finding Mass

• The mass of an object is measured with a triple beam balance.

• Mass is the amount of matter present in any given object.

• The standard unit for mass is grams (g) or kilograms (kg).

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Volume of Regular Shapes

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Volume of Irregular Shapes

• Use the water displacement method to find the volume of irregular objects.

• Place the object in a graduated cylinder that is filled with water.

• The volume is the difference in final and initial water levels.

Multiple Choice

An object is dropped into a graduated cylinder that contains 50 mL of water. The water level rises to 75 mL. What is the volume of the object?

• 25 mL

• 50 mL

• 75 mL

• 125 mL

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Will It Float or Sink?

Why It Floats

• An object will float if it is less dense than the liquid it is placed in.

• The density of pure water is a benchmark, which is about 1 gram per cubic centimeter (1 g/cm³).

• For example, ice has a density of 0.93 g/cm³, which is why it floats in water.

Why It Sinks

• An object will sink if it is more dense than the liquid it is placed in.

• This means its density is greater than water's density of 1 gram per cubic centimeter (1 g/cm³).

• For example, aluminum has a density of 2.7 g/cm³, which causes it to sink in water.

Multiple Choice

The density of oak wood is 0.85 g/cm³. Will a block of oak wood float or sink in water (density 1.0 g/cm³)?

• Float

• Sink

• It depends on the mass of the wood

• It depends on the volume of the wood

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Common Misconceptions

Misconception	Correction
Big or heavy objects always sink.	Floating is determined by density, not an object's size or weight.
Mass and density are the same thing.	Mass is the amount of matter; density is mass per unit volume.
Cutting an object in half also cuts its density in half.	Density is an intensive property and does not change with sample size.

Multiple Choice

A bar of copper has a mass of 216 g and a volume of 24 cm³. What is the density of copper?

• 9 g/cm³

• 0.11 g/cm³

• 192 g/cm³

• 5184 g/cm³

Multiple Choice

A block of wood has a density of 0.6 g/cm³ and a mass of 120 g. What is its volume? (Hint: Rearrange the density formula to solve for volume)

• 200 cm³

• 72 cm³

• 0.005 cm³

• 120.6 cm³

Multiple Choice

An irregularly shaped rock was lowered into a graduated cylinder holding 50 ml of water. The water rose to 75 ml. If the mass of the stone was 250 g, what was its density?

• 10 g/mL

• 3.3 g/mL

• 25 g/mL

• 250 g/mL

Multiple Choice

An irregularly shaped piece of gold was lowered into a graduated cylinder holding 17 ml of water. The water rose to 20 ml. If the mass of the gold was 57.9 g, analyze its density to determine if it's authentic gold (density of gold is 19.3 g/mL).

• The density is 19.3 g/mL, so it is authentic gold.

• The density is 3.4 g/mL, so it is not authentic gold.

• The density is 2.8 g/mL, so it is not authentic gold.

• The density is 37.9 g/mL, so it is not authentic gold.

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Summary

Poll

On a scale of 1-4, how confident are you about calculating density after this review?

• 1 (Not confident at all)

• 2 (A little confident)

• 3 (Mostly confident)

• 4 (Very confident)