Level 4 · Ages 13–15
Read it again any time, including while you work through the exercises.
A wooden cube and an iron cube of the same size do not have the same mass at all: iron is much heavier. Why? Because the matter in iron is more tightly packed: in the same volume, there is more mass. This idea is measured by density.
Density, written ρ (the Greek letter rho), is the mass of one unit of volume of a material. You compute it by dividing mass by volume: ρ = m ÷ V. It is often expressed in grams per cubic centimetre (g/cm³) or kilograms per cubic metre (kg/m³).
It is a quotient quantity, just like speed: speed tells you how many kilometres per one hour, density tells you how many grams per one cubic centimetre. Each material has its own: water is 1 g/cm³, aluminium 2.7 g/cm³, iron 7.8 g/cm³, oil about 0.9 g/cm³.
The formula flips every way you need: m = ρ × V to find a mass, and V = m ÷ ρ to find a volume. A magic triangle m, ρ, V, just like for speed!
Density explains many everyday mysteries: oil floats on water because it is less dense, an ice cube floats, a stone sinks. Your turn to crack these secrets by calculation!
A metal block has a volume of 200 cm³ and a mass of 540 g. Find its density. Which metal could it be?
ρ = m ÷ V
I write the formula: density is mass divided by volume.
ρ = 540 ÷ 200
I plug in the values from the problem.
ρ = 2,7 g/cm³
540 ÷ 200 = 2.7: each cubic centimetre of this metal weighs 2.7 g. That is the density of aluminium!
Result: ρ = 2.7 g/cm³: it is probably aluminium.
Oil has a density of 0.9 g/cm³. What is the mass of 250 cm³ of oil?
m = ρ × V
I am looking for a mass: I flip the formula into m = ρ × V.
m = 0,9 × 250 = 225
Each cm³ weighs 0.9 g, so 250 cm³ weigh 225 g. Check: it is indeed a bit less than 250 g, the mass the same amount of water would have.
Result: The 250 cm³ of oil weigh 225 g.