Density
Density as mass per unit volume, measuring it for regular and irregular solids and for liquids, and floating.
Review these first
Learning objectives
What you need to be able to do
Teacher-mapped phrasing — check against the official Cambridge syllabus for exact wording.
- 1.4.1Define density and recall and use ρ = m / V.
- 1.4.2Describe how to determine the density of a liquid, a regularly shaped solid and an irregularly shaped solid.
- 1.4.3Predict whether an object will float based on density data.
6 minute read
Density
Density is mass per unit volume: ρ = m / V, usually in kg/m³ or g/cm³ (1 g/cm³ = 1000 kg/m³).
Measuring density
The method depends on the shape:
Regular solid (a cube, cylinder): measure the mass with a balance. Measure the dimensions with a ruler or vernier calipers and calculate the volume from the shape's formula. Then ρ = m / V.
Irregular solid (a stone): measure the mass with a balance. Find the volume by displacement — lower the object into a partly filled measuring cylinder and read the rise in water level, or use a displacement can and collect and measure the overflow.
Liquid: measure the mass of an empty measuring cylinder, then the mass with a known volume of liquid in it. Subtract to find the mass of the liquid, and divide by the volume.
Predicting floating
An object floats in a fluid if its density is less than the density of the fluid, and sinks if its density is greater. Ice (about 0.92 g/cm³) floats on water (1.0 g/cm³) because it is less dense — this is why icebergs float with most of their bulk underwater.
Think of it like this
Density is how "packed" something is, not how big it is. A large beach ball and a small pebble can have very different densities even though the ball is bigger — it is mass squeezed into space that matters, not size alone.
Worked examples
Method, step by step
An irregular rock has a mass of 156 g. When lowered into a measuring cylinder, the water level rises from 40 cm³ to 80 cm³. Calculate the density of the rock.
- 1Volume of rock = volume displaced = 80 − 40 = 40 cm³
- 2ρ = m / V
- 3ρ = 156 / 40
ρ = 3.9 g/cm³
Common misconceptions
- Confusing density with mass or weight. A large but low-density object (polystyrene) can have less mass than a small, dense one (a lead ball).
- Forgetting to subtract the empty measuring cylinder's mass when finding the density of a liquid.
- Assuming all solids sink and all gases float — it depends entirely on comparing the two densities involved, not the state of matter.
In the exam
- State the displacement method precisely: "the volume of water displaced equals the volume of the object" is the key sentence markers look for.
- Always check your units are consistent — mixing g and kg, or cm³ and m³, is the most common way to lose an otherwise correct density calculation.