Two ideas that look similar on paper but mean very different things. By the end you'll never confuse density (how packed the matter is) with pressure (how concentrated a force is).
This mini-lesson sticks to exactly what CCEA GCSE Physics asks for — no more, no less:
Density — the equation density = mass ÷ volume, its units, and how to measure it (Prescribed Practical P4 + the displacement method).
Pressure — the equation P = F ÷ A, the unit pascal, and why a sharp knife or a caterpillar track works.
Heads-up: CCEA does not include pressure-in-liquids (p = hρg), hydraulics, atmospheric pressure or upthrust at GCSE — those belong to other boards or to A-Level. We keep strictly to the CCEA statements so nothing you revise here is wasted.
Density · what it means
How tightly is the matter packed?
Density tells you how much mass is squeezed into each unit of volume. A block of lead and a block of cork can be exactly the same size, yet the lead is far heavier — because lead's particles are heavier and more closely packed.
density = mass ÷ volume
ρ = m ÷ V · mass in g or kg · volume in cm³ or m³
CCEA accepts density in two unit pairs — match the unit to the units you put in:
mass in g, volume in cm³ → density in g/cm³
mass in kg, volume in m³ → density in kg/m³
Watch out: density does not depend on how much you have. Snap a chocolate bar in half and each piece has half the mass and half the volume — the density is unchanged. Density is a property of the material, not the lump.
Quick check
Same stuff, different size
?A solid gold bar is cut exactly in half. What happens to the density of each half compared with the original bar?
Density · Prescribed Practical P4
Measuring density: regular solids & liquids
CCEA's Prescribed Practical P4 investigates the link between mass and volume for liquids and regular solids. The recipe is the same each time: find the mass, find the volume, divide.
Mass from a balance, volume from a measuring cylinder (liquids) — then ρ = m ÷ V.
Liquid: mass it on a balance (subtract the empty beaker), pour it into a measuring cylinder and read the volume at the bottom of the meniscus.
Regular solid (cube, sphere, cylinder): mass it on a balance, then calculate its volume from measured lengths with a ruler — e.g. a cube is side³.
Examiner tip: read the measuring cylinder at eye level, at the bottom of the curved surface (the meniscus). Reading from above gives a volume that's too small and a density that's too big.
Calculate
Your turn — density of a metal cube
1A metal cube has a mass of 54 g and each side measures 3 cm. Calculate its density.
g/cm³
Hint: volume of a cube = 3 × 3 × 3 = 27 cm³, then ρ = m ÷ V.
Density · irregular solids
The displacement method
How do you find the volume of an awkward shape — a stone, a key, a small statue? You can't measure its sides. CCEA wants you to use the displacement method: the object pushes aside its own volume of water.
Lower the solid in; the water it pushes out equals the solid's volume. Mass it on a balance, then ρ = m ÷ V.
Fill a eureka can to the spout. Lower the solid in gently on a thread; catch the overflow in a measuring cylinder. That overflow volume = the solid's volume.
Or: part-fill a measuring cylinder, read the level, drop the solid in, read the new level — the rise is the solid's volume.
CCEA specifies this only for a solid that sinks in water — a floating object wouldn't push aside its full volume.
Watch out: the displacement method gives you volume, never density directly. You still need the balance for the mass before you can divide.
Calculate
Your turn — density of a pebble
2A pebble has a mass of 50 g. Lowered into a measuring cylinder, it raises the water level from 30 cm³ to 50 cm³. Calculate the pebble's density.
Once you know a material's density, the same equation gives you mass or volume. Cover the quantity you want in the triangle:
m = ρ × V | V = m ÷ ρ
If density is in kg/m³, keep mass in kg and volume in m³.
For example, water has a density of 1000 kg/m³ (the same as 1 g/cm³). So 1 m³ of water has a mass of 1000 kg — a tonne.
Watch out: don't mix unit systems in one sum. If you put kg into a sum that expects cm³, the answer is meaningless. Either work fully in g and cm³, or fully in kg and m³.
Calculate
Your turn — find the mass
3Aluminium has a density of 2.7 g/cm³. Calculate the mass of an aluminium block of volume 40 cm³.
g
Hint: rearrange ρ = m ÷ V to m = ρ × V = 2.7 × 40.
Quick check
Why steel ships don't sink
?Solid steel sinks in water, yet a huge steel ship floats. Which statement explains this best, using density?
Pressure · what it means
Force spread over an area
Pressure is the force pushing on each unit of area. Press a drawing pin: the same push from your thumb is concentrated onto a tiny point, so the pressure under the point is enormous — enough to pierce wood.
P = F ÷ A
pressure (Pa) = force (N) ÷ area (m²) · 1 Pa = 1 N/m²
CCEA defines pressure as the force exerted per square metre, with the unit named the pascal (Pa), where 1 Pa = 1 N/m².
Watch out: pressure is not the same as force. The same force gives high pressure on a small area and low pressure on a large area. That single idea explains both why a knife cuts and why a camel doesn't sink into sand.
Quick check
Sharp vs blunt
?You push a sharp knife and a blunt knife into bread with the same force. Why does the sharp knife cut more easily?
Pressure · everyday situations
Big area, small area
CCEA asks you to interpret pressure in everyday situations. The trick is always the same — ask whether you want high pressure (so make the area small) or low pressure (so make the area big).
Same physics, opposite goals: a pin maximises pressure; a caterpillar track minimises it.
Sharp knife / drawing pin / studs: small area → large pressure → easy to cut or pierce.
Caterpillar tracks / snowshoes / wide tyres: weight spread over a large area → small pressure → won't sink into soft ground.
Examiner tip: CCEA notes you may be given areas in cm² or mm² — you will not be asked to convert these to m². Just put the numbers straight into P = F ÷ A and quote the matching unit (e.g. N/cm²).
Calculate
Your turn — pressure under a box
4A crate exerts a downward force of 600 N on the floor through a base of area 3 m². Calculate the pressure on the floor.
Pa
Hint: P = F ÷ A = 600 ÷ 3.
Calculate
Your turn — find the force
5The flat heel of a shoe has area 0.002 m² and presses on the floor with a pressure of 250 000 Pa. Calculate the force on the floor.
N
Hint: rearrange P = F ÷ A to F = P × A = 250000 × 0.002.
Tie it together
Match each idea to its meaning
One last sort before the finish line. Match each CCEA term on the left to its correct description on the right.
Recap
Lock it in
Density ρ = m ÷ V · units g/cm³ or kg/m³ · measure mass on a balance, volume by ruler (regular) or displacement (irregular, sinks in water) · this is Prescribed Practical P4.
Pressure P = F ÷ A · unit pascal, 1 Pa = 1 N/m² · small area → big pressure (knife, pin); large area → small pressure (tracks, snowshoes).
Three traps to dodge: density doesn't change when you cut a material; pressure is not the same as force; and a dense material can still float if its average density (with trapped air) drops below the liquid's.
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