Volume · Year 6
In Volume (Year 6) you practise 4 skills: The volume of a box · The volume of a prism · Units of volume · Filling a box with cubes and books. Volume is how much space a solid takes up. To find the volume of a box, you can fill it with 1 cm³ cubes and count them in layers. One layer holds the length times the width, and there are as many layers as the height. So the volume of a box is the length times the width times the height.
The volume of a prism is also the area of its base times its height. When you know the volume and the height, divide the volume by the height to get the area of the base. When you fill a box with bigger cubes, check each edge on its own: how many cubes fit along it. A box 6 cm by 4 cm by 8 cm cannot be filled with cubes whose edges are 4 cm, because only one cube fits along the 6 cm edge, and a gap of 2 cm is left. Small things are measured in cm³, containers such as a bottle or a bucket in litres, and big things such as a room or a pool in m³. A litre is 1,000 cm³, and a millilitre is one cm³.
Tip: Write the unit at every step: cm for a length, cm² for the area of the base and cm³ for the volume.
What you learn
The volume of a box
For example: A box 6 long, 2 wide and 1 high is built from unit cubes. How many cubes are in it?
Answer and solution
The answer: 12
The layer has 2 rows, with 6 cubes in each row: 6 × 2 = 12
The volume of a prism
For example: The base of the prism has an area of 58 cm², and the prism is 3 cm high. What is the volume, in cm³?
Answer and solution
The answer: 174 cm³
The volume of a prism is the area of its base times its height. 58 × 3 = 174 The volume of the prism is 174 cm³.
Units of volume
For example: Which unit is best for measuring the volume of a sugar cube?
- Litres
- m³
- cm³
Answer and solution
The answer: cm3
A sugar cube is very small, so its volume is measured in cm³.
Filling a box with cubes and books
For example: The box is 3 cm long, 10 cm wide and 2 cm high. It is filled with cubes whose edges are 1 cm. How many cubes go in?
Answer and solution
The answer: 60
One layer has 10 rows of 3 cubes: 3 × 10 = 30 There are 2 layers: 30 × 2 = 60
The exercises are made by rules and the answers are worked out in code, so there are new exercises every time. The topic follows the national curriculum in England: mathematics (key stages 3 and 4).