Density, Mass and Volume, Grade 8
Density is measured, not felt.
Most Grade 8 classes meet density by holding two blocks and deciding which one feels heavier. That ranks things of the same size. It cannot give a number, and it cannot compare a small heavy thing with a large light one. A balance, a caliper and a displacement vessel can, and this page shows three ways to use them.
The density formula
density = mass ÷ volume, or ρ = m / V
The symbol ρ is the Greek letter rho. Rearranged, m = ρ × V and V = m ÷ ρ.
| Quantity | Unit in class | SI unit |
|---|---|---|
| Mass | g | kg |
| Volume | cm³, the same as ml | m³ |
| Density | g/cm³ | kg/m³ |
1 g/cm³ = 1 000 kg/m³.
How to calculate density: a worked example
A metal block has a mass of 54 g and a volume of 20 cm³.
ρ = 54 ÷ 20 = 2,7 g/cm³. The table below says that is aluminium.
The density of water
Water has a density of 1 g/cm³, which is 1 000 kg/m³. Strictly that is pure water at 4 °C; at room temperature it is 0,998, which rounds to the same thing.
It is why 1 ml of water has a mass of 1 g, and 1 litre has a mass of 1 kg, and it is the reference every other density is compared with.
Relative density
Relative density = density of a material ÷ density of water. It has no units. Aluminium has a relative density of 2,7. Anything with a relative density below 1 floats on water.
Reference densities
| Material | g/cm³ |
|---|---|
| Air, room temperature | 0,0012 |
| Pine | about 0,5 |
| Oak | about 0,75 |
| Polypropylene | 0,90 |
| Cooking oil | 0,92 |
| Ice | 0,92 |
| Water | 1,00 |
| Golden syrup | about 1,4 |
| Sand grains, quartz | 2,65 |
| Aluminium | 2,70 |
| Zinc | 7,14 |
| Iron | 7,87 |
| Brass | about 8,5 |
| Copper | 8,96 |
| Lead | 11,3 |
| Gold | 19,3 |
Why some materials are denser than others
| Reason | Example |
|---|---|
| How heavy the particles are | Gold and aluminium are both closely packed metals. A gold atom is about seven times heavier than an aluminium atom, and gold is about seven times denser |
| How closely they are packed | Steam is over a thousand times less dense than liquid water |
| Trapped air | Wood, sponge, bread, polystyrene and flour are light because they are mostly air. The cell walls of wood are about 1,5 g/cm³, denser than water. Wood floats because of the air in its cells |
The third one is the easiest to miss, and it explains most of the everyday examples a class comes up with.
A figure worth checking. A wooden block 10 cm on each side, 1 000 cm³, has a mass of about 500 g. You may meet the same block given as 4 kg. That works out to 4 g/cm³, denser than aluminium, and the block would sink.
Where this fits in the curriculum
| Subject | Natural Sciences |
|---|---|
| Grade | 8 |
| Term | 2 |
| Strand | Matter and materials |
| Topic | Particle model of matter: density |
| Status | Informal activities |
| Marks | 45 on our worksheet. None prescribed |
Practical 1: density of a regular solid
You need: a set of 20 mm density cubes, a vernier caliper and a balance that reads to 0,1 g.
- Measure all three sides of a cube with the caliper, to 0,1 mm, and convert to cm
- Multiply them to get the volume
- Weigh the cube, to 0,1 g
- Divide mass by volume, and find the material in the table
A 20 mm cube is 8,0 cm³. Aluminium should weigh about 21,6 g, iron about 63 g, copper about 72 g, and pine about 4 g.
Why a caliper and not a ruler? A ruler reads a 20 mm side to about half a millimetre. That is 2,5 % on each side and about 7,5 % on the volume, because the error is multiplied three times. Zinc at 7,14 and iron at 7,87 are too close to separate that way. A caliper reading to 0,1 mm brings it under 2 %.
And why measure every side? School cubes are made to about 5 %, so a "20 mm" cube may be 19,6 mm. Measure it rather than assume it.
A kitchen scale will not do. A 20 mm pine cube weighs about 4 g, so a scale that reads to 1 g is a 25 % error.
Practical 2: density of an irregular solid, by displacement
You need: a displacement vessel, sometimes called a eureka can, a 100 ml measuring cylinder, thread, and an object that sinks: a stone, a bolt, a lump of modelling clay.
- Fill the vessel above the spout and let it drip until it stops. Only now is it full exactly to the spout
- Put the empty cylinder under the spout
- Lower the object in on the thread. Do not drop it; a splash out of the top is water you will not measure
- When the dripping stops, read the cylinder. That volume is the volume of the object
- Dry and weigh the object, then divide
For a small object, the cylinder alone does it: read the level, drop the object in, read again. The rise is the volume.
Practical 3: sand and flour, loose and packed
You need: a 250 ml measuring cylinder, the balance, dry sand and cake flour.
- Weigh the empty cylinder
- Spoon sand in loosely to 200 ml. No tapping. Weigh it
- Tap the base on the bench twenty times. The level drops. Top up to 200 ml, tap again, and weigh
- Work out the density both times. Then do the same with flour
| Loose | Tapped | |
|---|---|---|
| Dry sand | about 1,45 g/cm³ | about 1,65 g/cm³ |
| Cake flour | about 0,55 g/cm³ | about 0,75 g/cm³ |
Neither answer is "the density of sand". A sand grain is quartz at 2,65 g/cm³. A cylinder of sand is grains plus air, and what you measured is its bulk density, which changes with how firmly it is packed.
That is why comparing cups of sand and flour by how heavy they feel is not a fair test. Two people filling the same cup differently get different answers. Packing has to be controlled.
Practical 4: the density column
A demonstration, in a 250 ml measuring cylinder.
- Pour in about 50 ml of golden syrup
- Tilt the cylinder and run 50 ml of coloured water slowly down the inside wall
- Do the same with 50 ml of cooking oil
- Drop in small objects one at a time: a plastic bottle cap, a grape, a cork, a steel nut
Three layers form, densest at the bottom, and each object stops at the layer that matches its density. The cork floats on the oil. The grape, about 1,1, rests between the water and the syrup. The nut goes straight to the bottom.
The point: heavy is not the same as dense. A big block of wood weighs more than a steel nut, and the wood floats while the nut sinks.
Afterwards, let the column settle and scoop the oil off into a bag for the bin. Oil does not go down the drain.
Solid, liquid, gas, and the one exception
For one substance, the gas is the least dense, and the solid is usually the densest, because its particles are packed closest.
The exception is water. Ice, at 0,92 g/cm³, is less dense than liquid water. Freezing locks the molecules into an open six-sided pattern with more space in it than the liquid has. That is why ice floats, why a pond freezes from the top down, and why the fish survive underneath. Liquid water is densest at about 4 °C.
Wood floating on water is sometimes given as the exception. It is not one. Wood and water are different substances, and the rule is about one substance changing state. For what happens while water melts and boils, see heating and cooling curves of water.
Heating lowers density
Heat a material and its particles move faster and take up more room. The number of particles stays the same, so the mass stays the same. The volume grows, so the density falls.
| Air at 20 °C | Air at 60 °C | |
|---|---|---|
| Density | 1,20 kg/m³ | about 1,06 kg/m³ |
That is why hot air rises, why a hot-air balloon flies, and why the warm air from a heater collects at the ceiling. Not because "heat rises": heat is not a substance. Hot air is less dense.
If it does not work
| Problem | Cause | Fix |
|---|---|---|
| The cube density matches nothing | Sides left in mm, or measured wrongly | 20 mm = 2,0 cm, and 2,0 × 2,0 × 2,0 = 8,0 cm³ |
| A metal cube is a few percent off | Cubes are made to about 5 %, and some are alloys | Choose the closest material |
| Displacement gives too little water | The vessel was not full to the spout | Fill above the spout and let it drip dry first |
| Displacement gives too much water | The object was dropped and splashed | Lower it on a thread |
| The sand result keeps changing | Packing | That is the result. Record loose and tapped separately |
| The column layers mix | Poured too fast | Run each liquid down the inside wall of the tilted cylinder |
Safety
- Nothing is tasted, including the syrup
- Glass displacement vessels break. Lower objects in on a thread
- Flour dust burns in a cloud. Spoon it, do not shake it about, and keep it away from flames
- Metal cubes are heavy for their size. Keep them off the bench edge
- Oil goes in the bin, not the sink
How the 45 marks are made up
| Section | Marks |
|---|---|
| The formula | 10 |
| Regular solids | 12 |
| An irregular solid | 8 |
| Sand and flour | 6 |
| Explain | 9 |
No mark allocation is prescribed for density. The worksheet and this split are ours.
Free worksheet and marking memo
Both free, no sign up, straight to the PDF.
- Learner worksheet, 45 marks, with a reference table, results tables for all three methods and five explain questions
- Marking memorandum, with what each cube should weigh, the range to accept for sand and flour, and the five answers that look right and score nothing
Related practicals
- Atoms, elements, compounds and mixtures, Grade 8. What the particles actually are
- Heating and cooling curves of water. Ice to steam, and why the temperature stops while it changes state
- Separating mixtures. Some of which work because of density
What you need to run it
The one item that turns this from feeling into measuring is the balance. Most schools already have one. If yours reads only to 1 g, a 0,1 g electronic balance is the upgrade that matters.
After that: a set of twelve 20 mm density cubes shared between four groups, a displacement vessel and a vernier caliper per group, and plastic measuring cylinders, which survive being knocked over. Everything else is sand, flour, syrup and oil from the kitchen.
The full range is in density equipment for schools.