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Year 4 Maths Volume & Capacity

Measure volume with cubic units

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Theory

Measuring volume with cubic units is a Year 4 measurement skill: volume is the space a solid takes up, and you find it by counting how many equal unit cubes fill the shape. This Year 4 maths page explains counting cubes, building solids in layers, using cubic centimetres, and seeing that different shapes can have the same volume. In the Australian and Victorian Curricula, counting cubes to find volume appears in Year 4 as part of making and describing objects; volume becomes a named skill in Years 5 and 6. Curriculum: VC2M4SP02 / AC9M4SP01.

Volume is the amount of space a solid object takes up. To measure it, we count how many equal cubes fill the object. The answer is a number of cubes, also called cubic units.

A unit cube is a cube that is the same size on every side. When each side is 1 centimetre, one cube takes up one cubic centimetre, written \(\text{cm}^3\). Volume is counted in cubes, just as length is measured in centimetres.

Solids are often built in layers. Count how many cubes are in one layer, then count how many layers there are. Two solids that use the same number of cubes have the same volume, even if they are different shapes.

A single unit cube one centimetre on each side One unit cube with each edge labelled 1 cm. A cube that is 1 cm long, 1 cm wide and 1 cm high has a volume of one cubic centimetre. 1 cm 1 cm 1 cm
One centimetre cube has a volume of 1 cubic centimetre.
A box built from twenty unit cubes in two layers A rectangular box built from unit cubes, 5 cubes long and 2 cubes deep in each layer, stacked 2 layers high, giving 20 cubes in total.
Two layers of 10 cubes make a volume of 20 cubes.

Volume does not need a hard formula in Year 4, but these facts help you count cubes quickly.

\[ \text{volume} = \text{number of unit cubes} \]
volume=number of unit cubes
\[ \text{volume} = \text{cubes in one layer} \times \text{number of layers} \]
volume=cubes in one layer×number of layers
\[ 10 \text{ cubes} \times 2 \text{ layers} = 20 \text{ cubes} \]
10×2=20
One cubic centimetre is the space taken up by a cube 1 cm long, 1 cm wide and 1 cm high. We write it as \(\text{cm}^3\), so a box filled with \(20\) centimetre cubes has a volume of \(20\text{ cm}^3\).
Moving cubes does not change the volume. If you pull a solid apart and build a new shape (even a tower \(1\) cube wide and \(1\) cube deep) with all the same cubes, the volume stays the same. Length is measured in cm, area in \(\text{cm}^2\) and volume in \(\text{cm}^3\).

How to measure a volume in cubes

  1. Look for the cubes. Check the solid is built from equal cubes with no gaps, including any hidden at the back.
  2. Count one layer. Find how many cubes are in a single layer of the solid.
  3. Count the layers. Multiply the cubes in one layer by the number of layers to get the total number of cubes.
  4. Long, wide and high. If you know how many cubes fit along, across and up, then one layer is along \(\times\) across, and the volume is one layer \(\times\) the number of layers. To find the number of layers, divide the volume by the cubes in one layer.
Example 1 — Count a row
Five equal cubes are joined in one row. What is the volume, in cubes?
A row of five unit cubes Five equal cubes joined end to end in a single row, giving a volume of 5 cubes.
Solution
\(\text{count the cubes}\)\(1, 2, 3, 4, 5\)
\(\text{volume}\)\(=\)\(5\text{ cubes}\)
volume=5 cubes

The volume is \(5\) cubes.

Example 2 — Three layers
This stack has 3 layers, and each layer has 3 cubes. What is the volume, in cubes?
A wall of cubes, three long and three high A stack of unit cubes with three layers, each layer holding 3 cubes, giving a volume of 9 cubes.
Solution
\(\text{one layer}\)\(=\)\(3\text{ cubes}\)
\(3\text{ layers}\)\(=\)\(3 + 3 + 3 = 9\)

The volume is \(9\) cubes. This is the same as \(3 \times 3 = 9\).

Example 3 — A filled box
This box is packed full with centimetre cubes, with some hidden at the back. It is 2 cubes long, 3 cubes deep and 3 cubes high. Find the volume in \(\text{cm}^3\).
A box of cubes, two long, three deep and three high A rectangular box built from centimetre cubes, 2 cubes long and 3 cubes deep in each layer, stacked 3 layers high, giving 18 cubes in total.
Solution
\(\text{one layer}\)\(=\)\(2 \times 3 = 6\)
\(3\text{ layers}\)\(=\)\(3 \times 6 = 18\)

The volume is \(18\text{ cm}^3\).

Example 4 — Same volume, new shape
Model P is 4 layers of 5 cubes. Model Q is 2 layers of 10 cubes. Do they have the same volume?
Solution
\(\text{Model P}\)\(=\)\(4 \times 5 = 20\)
\(\text{Model Q}\)\(=\)\(2 \times 10 = 20\)

Both use \(20\) cubes, so they have the same volume even though the shapes look different.

Example 5 — Along, across and up
A box is packed full with centimetre cubes. The cubes fit \(6\) along, \(2\) across and \(3\) high. What is the volume of the box?
Solution
\(\text{one layer}\)\(=\)\(6 \times 2 = 12\)
\(3\text{ layers}\)\(=\)\(3 \times 12 = 36\)

The volume is \(36\text{ cm}^3\).

Example 6 — How many layers?
A prism made of centimetre cubes has a volume of \(28\text{ cm}^3\). Each layer has \(7\) cubes. How many layers does it have?
Solution
\(28 \div 7\)\(=\)\(4\)
\(4 \times 7\)\(=\)\(28\)

The prism has \(4\) layers. Check: \(4\) layers of \(7\) cubes is \(28\) cubes.

Common pitfalls

Count cubes, not faces. Watch out for counting the flat sides you can see. Volume is the number of cubes that fill the solid, not the number of faces.
Do not forget the hidden cubes. In a full stack, cubes behind the front are still there. Picture the layers and count every cube, even the ones you cannot see.
Multiply the layers, do not just add. Four layers of 5 cubes is \(4 \times 5 = 20\) cubes, not \(4 + 5 = 9\). Count one layer, then multiply by the number of layers.

Frequently asked questions

What is volume?

Volume is the amount of space a solid object takes up. You measure it by counting how many equal cubes fill the object.

How do you measure volume with cubes?

Count how many equal unit cubes fill the solid. It is often easier to count the cubes in one layer, then multiply by the number of layers.

What is a cubic centimetre?

A cubic centimetre is the space taken up by a cube that is 1 cm long, 1 cm wide and 1 cm high. It is written as \(\text{cm}^3\).

How do you find the volume of a box made of cubes?

Find how many cubes are in one layer, then count the layers. Multiply the cubes in one layer by the number of layers. For example, \(10\) cubes in a layer with \(2\) layers is \(20\) cubes.

Can two different shapes have the same volume?

Yes. If two shapes are built from the same number of cubes, they have the same volume even when they look different. \(4\) layers of \(5\) and \(2\) layers of \(10\) both make \(20\) cubes.

What is the difference between area and volume?

Area measures a flat surface and is counted in squares, such as \(\text{cm}^2\). Volume measures the space inside a solid and is counted in cubes, such as \(\text{cm}^3\).

Does the volume change if you rebuild the cubes into a tower?

No. If you use all the same cubes, the volume stays the same. \(20\) cubes make a volume of \(20\) cubes whether they form a box or a tower \(20\) cubes high.

How do you find how many layers a prism has?

Divide the volume by the number of cubes in one layer. A \(28\text{ cm}^3\) prism with \(7\) cubes in each layer has \(28 \div 7 = 4\) layers.

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