9.4 Density

When you wash rice, the light husk floats while the rice sinks; pour oil on water and the oil floats. We often say “lighter things float, heavier things sink” — but a huge steel ship floats while a tiny pebble sinks. So “heavy” can’t be the whole story. The real idea is density.

What Is Density? Think of a bus: a few passengers = low density; packed full = high density. Density is about how much matter is crammed into a space. Formally, density is the mass in a unit volume:

\text{Density} = \frac{\text{Mass}}{\text{Volume}}

A wooden stick and an iron rod of the same size feel very different — iron has more mass in the same volume, so it is denser.

Units and a useful trick

The SI unit of density is kilogram per cubic metre (kg/m³). For liquids and small objects we often use gram per millilitre (g/mL) or gram per cubic centimetre (g/cm³).

Water = 1, and “Relative Density” A handy fact: the mass of 1 mL of water is about 1 g, so water’s density ≈ 1 g/cm³. This makes water a natural yardstick. The relative density of a substance is how many times denser it is than water:

\text{Relative density} = \frac{\text{Density of substance}}{\text{Density of water}}

Aluminium (density 2.7 g/cm³) has a relative density of 2.7 — it’s 2.7 times denser than water. Relative density is just a number, with no units.

The Float-or-Sink Rule Compare an object’s density with water’s (≈ 1 g/cm³):

  • Denser than water (> 1 g/cm³) → it sinks.
  • Less dense than water (< 1 g/cm³) → it floats.

So oil floats (less dense), iron sinks (denser). (Density isn’t the only factor for every situation — a steel ship floats because of its shape — but for a solid lump in water, density tells the story.)

Use the calculator: enter a mass and volume, get the density, and see whether the object floats or sinks in water.

Density calculator — float or sink?
Density = mass ÷ volume. Compare with water (1 g/cm³).



Worked Example

A stone sculpture has mass 225 g and volume 90 cm³. Find its density. Will it float or sink in water?

\text{Density} = \frac{225\ \text{g}}{90\ \text{cm}^3} = 2.5\ \text{g/cm}^3.

Since 2.5 g/cm³ is greater than water’s 1 g/cm³, the sculpture sinks.