Draft explainer. Pending final review by Katalyst educators.
What is density?
Density tells you how much mass is packed into a given volume. Two objects can be the same size but have very different masses — a cube of wood and a cube of iron, for example. The iron cube is denser.
density (ρ) = mass (m) ÷ volume (V)Common units are grams per cubic centimetre (g/cm³) and kilograms per cubic metre (kg/m³). Note that 1 g/cm³ = 1000 kg/m³.
Floating and sinking
A solid object placed in a liquid will float if its density is less than the liquid’s, and sink if its density is greater. Water has a density of about 1.00 g/cm³.
A steel ship floats even though steel is far denser than water. That’s because the ship’s hull encloses a large volume of air, so the average density of the whole ship is less than that of water.
| Material | Approx. density (g/cm³) | In water it… |
|---|---|---|
| Air (room conditions) | 0.0012 | rises (bubbles) |
| Ice | 0.92 | floats |
| Water | 1.00 | — |
| Aluminium | 2.70 | sinks |
| Iron | 7.87 | sinks |
| Gold | 19.3 | sinks |
Worked examples
Example 1 — A wooden block
A block has a mass of 240 g and a volume of 300 cm³.
ρ = 240 g ÷ 300 cm³ = 0.80 g/cm³. This is less than 1.00 g/cm³, so it floats in water.
Example 2 — A metal cube
A cube has sides of 2.0 cm and a mass of 21.6 g.
V = 2.0 × 2.0 × 2.0 = 8.0 cm³, so ρ = 21.6 g ÷ 8.0 cm³ = 2.7 g/cm³. It sinks — and its density matches aluminium.
Check your understanding
1. A stone has a mass of 150 g and a volume of 60 cm³. What is its density?
150 ÷ 60 = 2.5 g/cm³. It sinks in water.
2. Why does ice float on water?
Ice (about 0.92 g/cm³) is less dense than liquid water (about 1.00 g/cm³), because water molecules form an open structure when they freeze.
3. If you cut a floating block of wood in half, does each half float?
Yes. Density is a property of the material — halving the block halves both mass and volume, so the density stays the same.