Density

Imagine two boxes of identical size. One is full of feathers; the other is full of steel ball bearings. They look the same — but lifting them tells you immediately the steel box has far more mass crammed into the same volume. The steel box is denser.

$\rho = \frac{m}{V}$

where ρ ("rho") is density, m is mass and V is volume. The standard SI units are kg/m³, but in MYP labs you will more often use g/cm³ because the numbers are friendlier:

Material	Density (g/cm³)	Density (kg/m³)
Air (room temp.)	0.0012	1.2
Cork	~0.24	240
Ice	0.92	920
Water (4 °C)	1.00	1 000
Aluminium	2.70	2 700
Iron	7.87	7 870
Lead	11.3	11 300
Gold	19.3	19 300

To convert: 1 g/cm³ = 1 000 kg/m³.

For a regular solid (cube, cuboid, sphere, cylinder), measure dimensions with a ruler or vernier calliper and use the geometry formula:

• Cube / cuboid: V = l × w × h
• Cylinder: V = π r² h
• Sphere: V = (4/3) π r³

For an irregular solid (a pebble, a metal nut), use the water-displacement method:

1. Fill a measuring cylinder partly with water and record the level V₁.
2. Carefully add the irregular object so it is fully submerged.
3. Record the new water level V₂.
4. The object's volume is V₂ − V₁.

The object must sink fully and must not absorb water. For a floating object, push it under with a thin metal rod (whose volume is negligible) or use a "Eureka can" overflow method.

Compare densities to predict floating or sinking. An object floats when its density is lower than the density of the fluid it sits in.

• A cork (0.24 g/cm³) floats in water (1.00 g/cm³).
• A steel nail (~7.87 g/cm³) sinks in water but a steel ship floats — because the ship's overall density (including the air inside its hull) is less than 1 g/cm³.
• Ice (0.92 g/cm³) floats on water — which is why lakes freeze from the top down, keeping fish alive beneath.

This is why shape matters, not just material. A pile of bricks sinks; a sealed empty box made of the same bricks would float if its total mass divided by its total volume (including the air inside) is less than 1 g/cm³.

For floating, the upthrust (buoyancy) from the fluid equals the object's weight. The fraction of the object submerged equals the ratio of the object's density to the fluid's density. Ice floats with about 92% under water because its density is 0.92 × water's density.