Density, Mass and Volume
The density formula is density = mass ÷ volume: 100 g in 50 cm³ gives 2 g/cm³. The density triangle puts mass on top, density and volume underneath, so you can rearrange it to mass = density × volume.
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What Is Density, Mass and Volume?
- Mass means how heavy something is (measured in g or kg).
- Volume means how much space something takes up (measured in cm³ or m³).
- Density means how packed something is (measured in g/cm³ or kg/m³).
The Density Triangle Trick
- The density triangle helps you choose the correct formula.
- Mass = Density × Volume, Volume = Mass ÷ Density, and Density = Mass ÷ Volume.
Finding Density
- To find density, divide mass by volume.
- , so the chocolate has a density of /cm³.
Finding Mass
- To find mass, multiply density by volume.
- , so the wooden block has a mass of .
Finding Volume
- To find volume, divide mass by density.
- , so the medal has a volume of .
Gold Bar Practice
- First find the volume by multiplying length × width × height.
- , so the gold bar has a volume of .
- , so the gold bar has a mass of .
Practice Questions
Test your understanding
A block of metal has a mass of and a volume of . Find its density.
Correct! 🎉 +10 pointsCorrect! 🎉 Worth 10 XPNot quite right
Use density = mass ÷ volume.
So .
The density is /cm³.
(Mass always goes on top. Dividing the other way round, , gives volume per gram, not density.)
A glass marble has a density of /cm³ and a volume of . Find its mass.
Correct! 🎉 +10 pointsCorrect! 🎉 Worth 10 XPNot quite right
Use mass = density × volume.
So .
The mass is .
(Keep track of the decimal point: , so .)
An aluminium bar has a mass of and a density of /cm³. Find its volume.
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Use volume = mass ÷ density.
So .
The volume is .
(Check the size of the answer: of aluminium at /cm³ does weigh g.)
A pine block has a mass of and a volume of . Find its density.
Correct! 🎉 +20 pointsCorrect! 🎉 Worth 20 XPNot quite right
Use density = mass ÷ volume.
So .
The density is /cm³.
(A common slip is to divide the wrong way round, . Mass always goes on top, and because the mass is smaller than the volume the density must be less than 1.)
A solid metal cube has a mass of and a density of /cm³. Find the length of one side of the cube.
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First find the volume using volume = mass ÷ density:
For a cube, volume = side × side × side, so the side is the cube root of the volume:
because .
The side length is .
(Two traps: stopping at the volume of , and thinking the cube root means dividing by 3.)
A steel ingot in the shape of a cuboid measures by by . Steel has a density of /cm³. Find the mass of the ingot.
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We aren't given the volume, so find it first.
For a cuboid, volume = length × width × height .
Then use mass = density × volume:
The mass is .
(All three measurements must be multiplied together: alone is only the area of one face.)
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Interactive Activity
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Frequently asked questions
The questions students bump into most on this topic
Density is how tightly packed something is: how much mass fits into each unit of space. Picture a brick and a sponge of the same size. They have the same volume, but the brick has far more mass in that space, so its density is higher. In GCSE maths, density = mass ÷ volume, measured in grams per cubic centimetre.
Mass is how heavy something is, in grams or kilograms. Volume is how much space it takes up, in cubic centimetres or cubic metres. Density is how much mass is packed into that space, in grams per cubic centimetre or kilograms per cubic metre. The three are linked by the density triangle, with mass on top.
Three forms of one rule. Density = mass ÷ volume. Mass = density × volume. Volume = mass ÷ density. The density triangle keeps them straight: mass on top, density and volume underneath. Cover the one you want; side by side means multiply, one above the other means divide the top by the bottom.
Divide the mass by the volume. A bar of chocolate with a mass of 100 g and a volume of 50 cm³ has density 100 ÷ 50 = 2 g/cm³. The same triangle finds the other two: a wooden block with density 0.8 g/cm³ and volume 500 cm³ has mass 0.8 × 500 = 400 g, and volume is mass ÷ density.
Grams per cubic centimetre, g/cm³, or kilograms per cubic metre, kg/m³. Each unit is a mass unit divided by a volume unit, matching the formula. Gold has a density of 19.3 g/cm³, so a 10 cm³ bar has a mass of 193 g. Water is 1 g/cm³, which is why anything denser than 1 g/cm³ sinks in it.
Work out the volume first from the measurements, then use the triangle. A small gold bar measures 5 cm by 2 cm by 1 cm, so its volume is 5 × 2 × 1 = 10 cm³. Gold’s density is 19.3 g/cm³, so the mass is 19.3 × 10 = 193 g. Always check the units match before you multiply.
What's next?
Found this one hard? Go one step back first. Feeling confident? Carry on to the next lesson.
