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P5 Area and volume foundations

volume of a cube

A cube has edge length 4 cm. Find its volume.

A 4 by 3 by 3 solid. Drawing is not to scale.433
One step of the worked solution to volume of a cube, drawn in pencil.
5 steps, drawn in pencil

See all 5 steps

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The pattern behind it: Area and volume foundations

Choose the matching base and perpendicular height, or count equal cube layers before multiplying dimensions.

In this one. A cube has equal length, width and height. Volume counts cubic units, so multiply the edge length three times.

Build from one layertrianglebase x perpendicular height / 2cuboidbase layer x number of layers

How to spot it

Look for shapes drawn on a dotted or squared grid, sharing a side or a vertex, with names like ABCD and ABE. Words like "grid", "dots" or "squares" alongside a request to compare areas or heights are the giveaway.

Common mistake

Children measure height by eye along the slanted side of a shape instead of counting the straight up-down grid distance from the base to the opposite vertex, which gives the wrong height whenever a side leans.

Try one like it

Standard area of a triangle A triangle has base 8 cm and perpendicular height 5 cm. Find its area.
All 18 with this pattern →

The 33 problem patterns

All 33 patterns, one to a page — the 19 behind Primary 5 and 6 word problems, and the skills the younger years are built on. The bar model, how to spot it in the question, and the mistake children make. A booklet you can print. Free.

A PDF, and a note when new solutions go up.