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P5 Area and volume foundations

liquid volume in a tank

A rectangular tank is 8 cm long, 5 cm wide and filled to a height of 6 cm. Find the volume of water.

A 8 by 5 by 6 solid. Drawing is not to scale.856
One step of the worked solution to liquid volume in a tank, 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. Use the height of the liquid, which may differ from the tank height. The water forms a cuboid.

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.