Mathematics Year 6: Volume: what it is and how we measure it
Mathematics, Year 6 (Portugal): Volume is the space an object takes up: you measure it by counting units, and the unit you pick changes the number.
Space that holds units
The volume of an object is the amount of space it takes up. To measure it, you count how many units of volume fit inside, with no gaps and no overlaps. The unit can be non-standard, like a building cube or half a cube, or standard: the cubic centimetre (cm³), the cubic decimetre (dm³) and the cubic metre (m³), which are cubes with edges of 1 cm, 1 dm and 1 m. Objects with different shapes can have the same volume.
The unit changes the number
Measure with a small unit and the number is big; measure with a big unit and it is small. So you must always say the unit, and to be understood by everyone you use the standard ones. Pick a suitable one: cm³ for a small object, dm³ or litres for a bottle or a fish tank, m³ for a room or a lorry load. One litre is exactly the volume of a cube with a 1 dm edge: 1 dm³ = 1 l.
Same space, different counts
Build a block 4 by 3 by 2 with cubes of 1 cm edge: 4 × 3 × 2 = 24 cubes, so 24 cm³. A flat block 6 by 4 by 1 also has 6 × 4 × 1 = 24 cubes: another shape, the same volume. Now take half a cube as the unit: the first block needs 24 × 2 = 48 units. The number doubled because the unit halved, not because the block grew. Finally, pour a 1 l bottle into a hollow cube with 1 dm edge: it fills it exactly, so 1 dm³ = 1 l.
Taller does not mean bigger
It is natural to judge volume by height: the tall, thin object looks like it holds more. But volume counts all the space, in length, width and height together. A tower of 1 by 1 by 8 cubes has 8 cubes. A low block of 2 by 2 by 3 cubes has 12. The tower is taller, the block has more volume. Before you compare, count the units in each, or measure with the same unit.
Bottles, rooms and small things
A carton of juice says 1 l on the label: that is a volume, the same as a cube 1 dm on each edge. The air in a classroom is measured in m³, because cm³ would give an enormous number. A small stock cube or a stone for a game is a matter of cm³. Each time, the trick is the same: pick a unit that gives a number you can imagine.
Test what you learned
Which sentence best says what the volume of an object is?
- a) The length of its longest edge
- b) The total area of the surface that covers it
- c) The space it takes up, measured by how many units fit in it
- d) How heavy it is
Correct answer: c) The space it takes up, measured by how many units fit in it — Yes: volume is the space occupied, and you measure it by counting units of volume with no gaps or overlaps.
A block made of 4 × 3 × 2 cubes has a volume of 24 cm³ (each cube has a 1 cm edge). Measured with half-cubes as the unit, how many units is that?
- a) 24
- b) 48
- c) 12
- d) 96
Correct answer: b) 48 — Right: each whole cube holds 2 half-cubes, so 24 × 2 = 48 units. Same volume, smaller unit, bigger number.
Ana builds a tower of 1 × 1 × 8 small cubes. Rui builds a low block of 2 × 2 × 3 of the same cubes. Whose construction has the larger volume?
- a) Rui's block: 12 cubes against 8
- b) Ana's tower, because it is taller
- c) Both have the same volume, they use the same cubes
Correct answer: a) Rui's block: 12 cubes against 8 — Yes: 2 × 2 × 3 = 12 cubes and 1 × 1 × 8 = 8 cubes. The lower block takes up more space.
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