Density, Mass & Volume
Grade 5What density tells you
Density is how much mass is packed into a given volume. A block of lead and a block of foam can be the same size, but the lead has much more mass crammed into it — it has higher density.
Density = Mass ÷ Volume
The standard unit is g/cm³ (grams per cubic centimetre) or kg/m³. The unit is a reminder of the formula: grams per cubic centimetre means grams divided by cm³.
Rearranging the formula
Just like speed, density uses a triangle. Put M at the top, and D × V at the bottom:
Mass = Density × Volume. Volume = Mass ÷ Density. Density = Mass ÷ Volume.
Think of density as the "rate" — it's how many grams you get per unit of volume. That framing makes the formula feel natural rather than something to memorise.
Worked example
EXAMPLE
A piece of metal has a mass of 540 g and a volume of 200 cm³. Calculate its density.
Density = Mass ÷ Volume = 540 ÷ 200 =2.7 g/cm³.
Finding volume from density
EXAMPLE
Gold has a density of 19.3 g/cm³. What volume would 386 g of gold occupy?
Volume = Mass ÷ Density = 386 ÷ 19.3 =20 cm³.
Units trap
If the question mixes units (mass in kg but volume in cm³), convert before you calculate. Using mismatched units gives a density figure that belongs to neither standard unit — and you'll lose marks even if your arithmetic is right.
