Use π = 3.141 litre = 1000 cm³Volume is measured in cubic units — cm³, m³r = radius (half the diameter)
Cuboid
V = lbh
Prism
V = Ah
A = area of the cross-section
Cylinder
V = πr²h
Cone
V = 13πr²h
Pyramid
V = 13Ah
A = area of the base
Sphere
V = 43πr³
Worked examples
A cone has a radius of 6 cm and a height of 14 cm.
Calculate the volume of the cone. Give your answer to 3 significant figures.(3 marks)
Calculate the volume of the cone. Give your answer to 3 significant figures.(3 marks)
V = 13πr²h
In plain EnglishFind the cone on the formula sheet and write it down. Writing it first stops you forgetting the ⅓.
V = 13 × 3.14 × 6² × 14 ✓1
In plain EnglishSwap each letter for its number: π = 3.14, r = 6 and h = 14. Write this line out in full. It earns the first mark.
V = 527.52 ✓2
In plain EnglishType it all into the calculator in one go. Write down the full answer before you round.
V = 528 cm³ ✓3
In plain EnglishRound to 3 significant figures: 527.52 becomes 528. Volume is measured in cubic units, so write cm³.
⚠ Radius, not diameter. If you are given the diameter, halve it first.
⚠ Don’t round too early. Only round on the very last line.
A toy is made from a hemisphere on top of a cone. Both have a radius of 4 cm. The cone has a height of 10 cm.
Calculate the volume of the toy. Give your answer to 3 significant figures.(5 marks)
Calculate the volume of the toy. Give your answer to 3 significant figures.(5 marks)
Toy = hemisphere + cone
In plain EnglishSplit the toy into two shapes you know: a hemisphere on top and a cone underneath. Find each one, then add them together.
Sphere
V = 43πr³
V = 43 × 3.14 × 4³ ✓1
In plain EnglishThere's no hemisphere formula, so start with the sphere: V = 4⁄3πr³. Put in r = 4. You'll halve it in a moment.
Cone
V = 13πr²h
V = 13 × 3.14 × 4² × 10 ✓2
In plain EnglishNow the cone: V = ⅓πr²h, with r = 4 and h = 10. Both shapes share the same radius.
Total = hemisphere + cone
V = 12 × 43 × 3.14 × 4³ + 13 × 3.14 × 4² × 10 ✓3
In plain EnglishA hemisphere is half a sphere, so multiply the sphere by ½. Then add the cone. Writing this line shows the marker you know what to do.
V = 133.9733... + 167.4666...
V = 301.44 ✓4
In plain EnglishWork it out using the full, unrounded numbers.
V = 301 cm³ ✓5
In plain EnglishRound to 3 significant figures and add the units: cm³.
⚠ Add or subtract? Add when parts are joined together. Subtract when a part is cut out or removed.
⚠ Don’t forget to halve. The most common error is using the full sphere instead of the hemisphere.
A cylindrical tin holds 1.5 litres. The radius of the tin is 6 cm.
Calculate the height of the tin. Give your answer to 1 decimal place.(3 marks)
Calculate the height of the tin. Give your answer to 1 decimal place.(3 marks)
1.5 litres = 1500 cm³
In plain English1 litre is 1000 cm³, so 1.5 litres is 1500 cm³. That's the volume.
V = πr²h
In plain EnglishThe tin is a cylinder, so use V = πr²h.
1500 = 3.14 × 6² × h ✓1
In plain EnglishThis time you know the volume and the radius. Put them in and leave h as the unknown.
1500 = 113.04h
In plain EnglishMultiply out the numbers you know: 3.14 × 6² = 113.04.
h = 1500 ÷ 113.04 = 13.2696... ✓2
In plain Englishh is being multiplied by 113.04, so divide both sides by 113.04. Write down the full answer.
h = 13.3 cm ✓3
In plain EnglishRound to 1 decimal place. It's a length, so the units are cm, not cm³.
⚠ Check your answer. Put h = 13.3 back into the formula: 3.14 × 36 × 13.3 ≈ 1503 cm³ ≈ 1.5 litres ✓
Every volume question: formula → substitute → full calculator answer → rounded answer with units.
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Your turn
Use π = 3.14 and a calculator. Units are optional when you type your answer, but always write them in the exam. Stuck? Tap Need a hint? for one clue at a time.
Past paper questions
Ready for exam-style questions? Use these links to practise volume questions from real SQA papers. Remember: formula → substitute → full answer → rounded answer with units.
Volume: past paper questions by topicEvery SQA past paper and specimen volume question (2014–2025) in one PDF, with answers. Start here.maths.scot Open ↗ (opens in a new tab) National 5 Maths: volume of a simple shapeSingle-shape volume questions from National 5 Maths papers, each with a link to its marking scheme.dynamicmaths.co.uk Open ↗ (opens in a new tab) National 5 Maths: volume of a composite shapeComposite shape volume questions from National 5 Maths papers, each with a link to its marking scheme.dynamicmaths.co.uk Open ↗ (opens in a new tab)