Density, Mass & Volume

Grade 5

What 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.

Try this one

A train travels at 90 km/h for 40 minutes, then at 60 km/h for 30 minutes.

(a) Find the total distance the train travels. [2]

(b) A car travels the same total distance in 1 hour 15 minutes. Find the average speed of the car in km/h. [2]

Nova's hint:

This uses speed, distance, time with unit conversion.

Ask yourself: 'Have I converted the times into hours before using Distance = Speed × Time?' For example, 20 minutes = 20/60 = 1/3 of an hour.

Try to Solve it with Nova?