C. Matter and Energy · Fluids

Mass, Volume and Density

C2.2 A1.2 A1.4About 50 minutes

Learning goals

I can explain the relationship between mass, volume and density.
I can calculate density using density = mass ÷ volume, and rearrange it to find mass or volume.
I can measure the volume of an irregular object by water displacement.
I can use density to help identify a substance.

Words to know

mass
The amount of matter in an object, measured in grams (g) or kilograms (kg) with a balance or scale.

volume
The amount of space an object or substance takes up, measured in millilitres (mL), litres (L) or cubic centimetres (cm³). 1 mL = 1 cm³.

density
The mass of a substance in a certain volume. Density = mass ÷ volume, in units such as g/mL, g/cm³ or kg/m³.

displacement
A way to find the volume of an object by measuring how much water it pushes aside (how much the water level rises) when it is put in water.

characteristic property
A property, like density, that stays the same for a pure substance no matter how big the sample is, so it can help identify the substance.

A heavy question

Which is heavier: a kilogram of feathers or a kilogram of rocks? (Trick question: they have the same mass, 1 kg each!) But the feathers would fill a big garbage bag, and the rocks would fit in your hands.

The difference is density: how much mass is packed into each bit of space. In Grade 7 you learned that warm matter is less dense than cold matter. Now you'll learn to calculate density and use it like a scientist.

A big clear bag stuffed with white feathers next to a much smaller pile of grey stones on a table. — If the bag of feathers and the pile of rocks each had a mass of 1 kg, the feathers would still take up far more space. The rocks are much more dense. AI-generated image

Mass and volume

Mass is the amount of matter. Measure it on a balance or a kitchen scale, in grams (g) or kilograms (kg).
Volume is the amount of space something takes up. Measure liquids in millilitres (mL) or litres (L). Measure solids in cubic centimetres (cm³).
1 mL = 1 cm³. A cube 1 cm on each side holds exactly 1 mL.

For a box-shaped (rectangular) solid: volume = length × width × height.

Density

Density = mass ÷ volume

You can write it as D = m ÷ V.

If you know two of the three, you can find the third:

mass = density × volume (m = D × V)
volume = mass ÷ density (V = m ÷ D)

Units: if mass is in g and volume in mL, density is in g/mL. If volume is in cm³, density is in g/cm³. Engineers often use kg/m³. 1 g/cm³ = 1000 kg/m³.

Water has a density of about 1 g/mL. So 1 mL of water has a mass of about 1 g, and 1 L of water has a mass of about 1 kg. That makes water a handy number to remember.

The density triangle. Mass sits on top; density and volume sit side by side underneath, so mass = density × volume.

Substance	Approximate density (g/cm³ or g/mL)
air (room temperature)	0.0012
cork	0.24
cooking oil	0.92
ice	0.92
fresh water	1.00
sea water	1.03
maple syrup	1.33
honey	1.4
aluminium	2.7
iron	7.9
copper	9.0
gold	19.3

Approximate densities at room temperature. Each pure substance has its own density, so density can help identify it.

Worked example

Let's find the density of a block of wood

A rectangular block of wood is 5 cm long, 4 cm wide and 3 cm high. Its mass is 45 g. What is its density?

Step 1. Find the volume. V = 5 cm × 4 cm × 3 cm = 60 cm³.
Step 2. Write the formula. D = m ÷ V.
Step 3. Substitute. D = 45 g ÷ 60 cm³.
Step 4. Calculate. 45 ÷ 60 = 0.75.
Step 5. Add units and check. g/cm³. 0.75 is less than water's 1.00, so we predict the block floats. (You'll test that idea in the buoyancy lesson.)

The wood's density is 0.75 g/cm³.

Worked example

Let's find the density of a rock by displacement

A rock has a mass of 135 g. It is too lumpy to measure with a ruler. Liam puts 200 mL of water in a measuring cup, then gently lowers the rock in. The water rises to 250 mL. Find the rock's density.

Step 1. Find the volume by displacement. The rock pushed the water up by 250 mL − 200 mL = 50 mL, so the rock's volume is 50 mL = 50 cm³.
Step 2. Write the formula. D = m ÷ V.
Step 3. Substitute and calculate. D = 135 g ÷ 50 cm³ = 2.7 g/cm³.
Step 4. Interpret. That's a typical density for a common rock such as granite. (It also matches aluminium, which is why density alone can't always identify a material; you'd check other properties too.)

The rock's density is 2.7 g/cm³.

Displacement. The rock pushes the water up from 200 mL to 250 mL, so the rock's volume is 50 mL = 50 cm³. Then 135 g ÷ 50 cm³ = 2.7 g/cm³.

Same substance, same density

If you cut a chocolate bar in half, each half has half the mass and half the volume. Mass ÷ volume stays the same. A paper clip and a steel beam made of the same steel have the same density. That's why density is a characteristic property: it helps identify a substance, whatever the sample's size.

Heavy-duty fact

Osmium is one of the densest metals on Earth, about 22.6 g/cm³. A 2 L pop bottle filled with it would have a mass of about 45 kg (2000 cm³ × 22.6 g/cm³). Good luck carrying that to a picnic.

Hands-on activity

Kitchen density lab

You need: a kitchen scale (digital is best), a liquid measuring cup, water, cooking oil, and a small solid that sinks and won't be harmed by water (a clean rock, a metal spoon, or a potato). Paper, pencil and a calculator.

Part 1: density of water

Put the empty measuring cup on the scale. Press tare (or zero) so the scale ignores the cup's mass.
Pour in 250 mL of water. Read the mass.
Calculate D = m ÷ V.

Part 2: density of cooking oil

Tare a clean, dry cup. Add 100 mL of cooking oil. Read the mass and calculate the density. (Pour the oil back into its bottle with a grown-up's help or keep it for cooking. Never pour oil down the drain; it can help clog pipes.)

Part 3: density of a solid by displacement

Measure the solid's mass on the scale.
Fill the measuring cup to a line you can read, such as 300 mL. Gently lower the solid in (tilt the cup or use a string so nothing splashes). Read the new level. The rise is the solid's volume.
Calculate its density.

Record your results in a table: substance, mass, volume, density. Compare with the table in this lesson.

What to look for: water should be close to 1 g/mL, and oil close to 0.9 g/mL. Small differences come from reading the measuring cup. A potato is usually a little denser than water, so it sinks.

Safety: wipe up oil spills right away (slippery). Ask before using a kitchen scale, and keep it dry.

Your turn

Write the formula for density. What does each letter stand for?

An object has a mass of 200 g and a volume of 250 cm³. What is its density?

A block is 2 cm × 3 cm × 4 cm and has a mass of 21.6 g. What is its density?

The water in a measuring cup rises from 100 mL to 112 mL when a key is dropped in. What is the key's volume?

A tiny piece of copper and a big copper pot are made of the same copper. How do their densities compare?

What is the mass of 1 L of water? Why?

Convert 2.7 g/cm³ into kg/m³.

More practice: warm-up

10 g of a liquid has a volume of 10 mL. What is its density?

50 g, 25 cm³. Density?

How many cm³ are in 1 mL?

What tool measures mass?

Give one unit of density.

More practice: on your own

Maple syrup has a density of about 1.33 g/mL. What is the mass of 250 mL of maple syrup?

Iron has a density of 7.9 g/cm³. What volume does 79 g of iron take up?

A ring has a mass of 38.6 g. When lowered into water, it raises the level by 2.0 mL. What is its density? Which metal in the table does it match?

When you measure the mass of a liquid in a cup, why do you press "tare" with the empty cup on the scale first?

Two cubes are exactly the same size. Cube A has a mass of 30 g and cube B has a mass of 90 g. Which is denser? How many times as dense?

Challenge

A metal cube is 2 cm on each side and has a mass of 72 g. Use the table to identify the metal.

Which has more mass: 1 L of cooking oil (0.92 g/mL) or 1 L of water (1.00 g/mL)? By how much?

Zoe finds the density of a pebble by displacement, but some water splashes out of the cup when she drops the pebble in. Will her density answer be too high or too low? Explain.

Check your understanding

Quiz

Density is...

A 60 g object has a volume of 20 cm³. Its density is...

A stone raises the water in a measuring cup from 150 mL to 180 mL. Its volume is...

Water's density is about 1 g/mL. What is the mass of 500 mL of water?

A large and a small piece of the same aluminium have...

A material has a density of 4 g/cm³. What is the mass of 5 cm³ of it?

For parents and teachers

Big idea (C2.2): density is the relationship between mass and volume: D = m ÷ V. Students calculate density, rearrange the formula, and measure the volume of irregular objects by displacement. The kitchen lab practises measurement and safety (A1.2, A1.4).

How to help: use your kitchen scale and measuring cups. A litre of milk or water has a mass of about 1 kg. Ask: "Which takes up more space, 100 g of marshmallows or 100 g of sugar?"

Common difficulties:

Dividing the wrong way (volume ÷ mass). Remind them: density is mass per volume.
Mixing up "heavy" and "dense". A huge log is heavy but less dense than water. A tiny pebble is light but denser than water.
Forgetting units, or mixing mL and L.
Displacement errors: splashing, or reading the measuring cup from above instead of at eye level.

Safety: oil makes floors slippery. Don't pour oil down the drain.