L5 · What is volume: units and cubic centimetres

Learning goal

“I can describe volume as the number of unit cubes that fill a solid, count cubes in a rectangular arrangement (including the ones I cannot see), and measure volume in cubic centimetres (cm3).”

Volume — the amount of space a solid takes up, measured by how many unit cubes fill it.

Cubic unit — a cube used as the measuring unit; its size must be stated, because the count depends on it.

Cubic centimetre (cm3) — the volume of a cube 1 cm on each side; the standard unit in this unit.

Layer — one flat sheet of cubes in an arrangement; a solid is a stack of equal layers.

Worked example

A box is filled with centimetre cubes. The bottom layer is 3 cubes long and 2 cubes wide, and the cubes stack 2 layers high. Step 1: One layer holds 3 x 2 = 6 cubes. Step 2: There are 2 equal layers, so total cubes = 6 x 2 = 12 cubes. Step 3: Each cube is 1 cm3, so the volume is 12 cm3. Say it plainly: volume counts cubes that fill the space - including cubes hidden inside or behind, which you know are there because the layers are complete.

Check yourself — explain it

Why can we count cubes we cannot see?

Paired problem — example still visible

A single layer of cubes, 4 long and 2 wide, 1 layer high -> 4 x 2 x 1 = 8 cubes = 8 cm3

Faded completion — last step is yours

"Layers of 5 x 3 cubes, stacked 2 high: one layer = 15 cubes; total = 15 x ___ = ___ cm3" -> 2; 30 cm3

Ready to practise?

10 scored questions with a 3-rung hint ladder. Mastery needs 8/10 plus both gate questions.

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