Key ideas
Volume of a prism
A prism has the same shape all the way through.
Volume = area of the end × length
Volume is measured in cubic units: cm³, m³.
Cylinder
The end is a circle, with area πr².
V = πr²h
We use π = 3.14. If you are given the diameter, halve it first.
Triangular prism
The end is a triangle.
Area = base × height2
V = area of triangle × length
Litres
1 litre = 1000 cm³
To change cm³ into litres, divide by 1000.
Volume of a cylinder
Calculate the volume of this cylinder. Use π = 3.14.(3 marks)
Write the formula.V = πr²h
In plain EnglishThe end of a cylinder is a circle, so V = area of the circle × height.
Substitute.V = 3.14 × 5² × 12✓1
In plain Englishr = 5 and h = 12.
Calculate.V = 3.14 × 25 × 12✓2V = 942 cm³✓3
In plain EnglishSquare the radius first: 5² = 25. Then multiply. Volume is in cm³.
Cylinders from a diameter
Calculate the volume of this cylinder. Use π = 3.14.(3 marks)
Halve the diameter.r = 82 = 4 cm✓1
In plain EnglishThe formula uses the radius, so halve the diameter.
Substitute.V = 3.14 × 4² × 10✓2
In plain EnglishVolume = πr²h. Put in π = 3.14, r = 4 and h = 10.
Calculate.V = 3.14 × 16 × 10 = 502.4 cm³✓3
In plain EnglishSquare the radius first (4² = 16), then multiply. Volume is in cubic units: cm³.
⚠ A common mistake: using 8 as the radius. That gives 2009.6 cm³, four times too big.
Volume of a triangular prism
Calculate the volume of this triangular prism.(3 marks)
Area of the triangle.A = 6 × 82 = 482 = 24 cm²✓1
In plain EnglishThe end is a right-angled triangle with base 6 cm and height 8 cm. Area = base × height, divided by 2.
Multiply by the length.V = 24 × 15✓2V = 360 cm³✓3
In plain EnglishThe length of the prism is 15 cm.
Volume in context
A cylindrical tank has radius 20 cm and height 50 cm. How many litres of water does it hold? Use π = 3.14.(3 marks)
Volume.V = 3.14 × 20² × 50✓1V = 3.14 × 400 × 50 = 62 800 cm³✓2
In plain EnglishUse V = πr²h with r = 20 and h = 50. Square the radius first: 20² = 400.
Change to litres.62 8001000 = 62.8 litres✓3
In plain English1 litre = 1000 cm³, so divide by 1000.
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Your turn
Calculator allowed. Use π = 3.14 (an answer from the π button is marked right too). Remember the units: cm³ or m³. Stuck? Tap Need a hint?