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See Plans →Volume is the amount of three-dimensional space inside a shape. We measure it in cubic units — cm³, m³, mm³ — because we are multiplying three lengths together.
For a cuboid: \(V = l \times w \times h\)
You can picture it as layers: a 4 × 3 × 2 cuboid has 4 × 3 = 12 unit cubes per layer, stacked into 2 layers, giving 24 cm³.
Find the volume of a cuboid with dimensions 8 cm × 5 cm × 3 cm.
\(V = l \times w \times h = 8 \times 5 \times 3\)
\(8 \times 5 = 40\), then \(40 \times 3 = 120 \text{ cm}^3\)
A fish tank is 60 cm × 30 cm × 40 cm. Find its volume in litres.
\(V = 60 \times 30 \times 40 = 72\,000 \text{ cm}^3\)
\(72\,000 \div 1000 = 72 \text{ litres}\)
A prism is a 3D shape with an identical cross-section all the way along its length — like a Toblerone box (triangular prism) or a swimming pool channel.
Because every slice through the length is the same, we simply multiply that area by the length:
Triangular prism: \(V = \tfrac{1}{2} \times \text{base} \times \text{height} \times \text{length}\)
L-shaped prism: Split the cross-section into rectangles, find total area, then × length.
A triangular prism has a triangle base of 6 cm, perpendicular height 4 cm, and length 10 cm.
\(A = \tfrac{1}{2} \times 6 \times 4 = 12 \text{ cm}^2\)
\(V = A \times l = 12 \times 10 = 120 \text{ cm}^3\)
An L-shaped prism has cross-section split into an 8 × 5 rectangle and a 4 × 3 rectangle. Length = 12 cm.
\(8 \times 5 = 40 \text{ cm}^2\)
\(4 \times 3 = 12 \text{ cm}^2\)
\(40 + 12 = 52 \text{ cm}^2\)
\(V = 52 \times 12 = 624 \text{ cm}^3\)
A cylinder is a circular prism. Its cross-section is a circle of area \(\pi r^2\), so:
Real-life examples: drinks cans, water pipes, oil drums, silos, cylinders in engines.
Unit conversions to memorise:
A cylinder has radius 5 cm and height 12 cm. Find its volume in terms of \(\pi\) and as a decimal.
\(V = \pi r^2 h = \pi \times 5^2 \times 12\)
\(5^2 = 25\)
\(\pi \times 25 \times 12 = 300\pi \approx 942.5 \text{ cm}^3\)
A cylindrical water tank has diameter 1.2 m and height 2 m. Find its volume in litres.
\(r = \tfrac{1.2}{2} = 0.6 \text{ m}\)
\(V = \pi \times 0.6^2 \times 2 = \pi \times 0.36 \times 2 = 0.72\pi \text{ m}^3\)
\(0.72\pi \times 1000 \approx 2262 \text{ litres}\)
Enter your answer (to the nearest whole number where needed). Use 3.14159 for \(\pi\).
| # | Shape | Dimensions | Your Answer | Result |
|---|---|---|---|---|
| 1 | Cuboid | 6 cm × 4 cm × 5 cm | ||
| 2 | Cuboid | 3 m × 2 m × 1.5 m | ||
| 3 | Triangular prism | Triangle: base 10 cm, height 6 cm; length 8 cm | ||
| 4 | Cylinder | r = 4 cm, h = 9 cm | ||
| 5 | Cylinder | Diameter = 6 cm, h = 10 cm | ||
| 6 | Cuboid | 10 cm × 3 cm × 2 cm | ||
| 7 | Cuboid | 7 cm × 4 cm × 3 cm | ||
| 8 | Cylinder | r = 5 cm, h = 6 cm | ||
| 9 | Cylinder | r = 4 cm, h = 7 cm | ||
| 10 | Triangular prism | Triangle: base 8 cm, height 5 cm; length 10 cm |