Density
rho = m / V
The unit tells you what to divide by what — and cm^3 vs m^3 is the classic trap.
Know the equation
| Symbol | Quantity | Unit |
|---|---|---|
| rho | density | kg/m3 (or g/cm3) |
| m | mass | kg (or g) |
| V | volume | m3 (or cm3) |
Rearrangements
- m = rho x V
- V = m / rho
Apply it — mark your own working
Work each one out on paper first, then reveal the mark scheme and tick the marks you actually earned. That is exactly how you should mark past papers.
A block of metal has a mass of 780 g and a volume of 100 cm3. Calculate its density in g/cm3.
Do the calculation on paper first — then mark it.
Aluminium has a density of 2700 kg/m3. Calculate the mass of an aluminium block with a volume of 0.0020 m3.
Do the calculation on paper first — then mark it.
Where the marks get lost
- Dividing volume by mass instead of mass by volume — the unit (kg/m3) tells you it is mass over volume.
- Mixing unit systems: use g with cm3, or kg with m3, never one of each.
- Forgetting that 1 m3 = 1 000 000 cm3 when a question forces a conversion.
Exam tip: Read the unit the answer must be in and match your inputs to it: an answer in g/cm3 needs mass in g and volume in cm3, so no conversion is needed here.
Still losing marks on the calculations?
I'll go through your working line by line and show you exactly where the marks are — your first lesson is free.