A rectangular prism (a box shape) can be filled with layers of centimetre cubes. The bottom layer holds length × width cubes, and there are as many layers as the height. So volume = length × width × height, measured in cubic centimetres (cm³). Adding the lengths or finding the faces' areas does not give the volume. To find a missing length, multiply the two you know, then divide the volume by that answer.
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Maths you can move
Build 8 + 5
Tap two gold counters to fill the ten-frame.
8 in the frame + 5 waiting. The total stays the same.
Words to know
- rectangular prism
- a box shape with six rectangular faces
- cubic centimetre (cm³)
- the volume of a cube 1 cm long, 1 cm wide and 1 cm high
Worked examples
A prism is 5 cm long, 4 cm wide and 3 cm high. What is its volume?
- 1.Bottom layer: 5 × 4 = 20 cubes.
- 2.3 layers: 20 × 3 = 60 cm³.
= 60
A box is 12 cm long, 5 cm wide and 4 cm high. What is its volume?
- 1.12 × 5 = 60 in a layer.
- 2.60 × 4 = 240 cm³.
= 240
A prism has a volume of 60 cm³, a length of 5 cm and a width of 4 cm. What is its height?
- 1.5 × 4 = 20.
- 2.60 ÷ 20 = 3 cm.
= 3
For parents
Method: Length × width × height
What to say: How many cubes fit in the bottom layer? How many layers?
Common mistakes:
- Adds the length, width and height instead of multiplying.
- Multiplies only two of the dimensions, finding one layer (the base area) and stopping.
- Adds up the areas of the faces (surface area) instead of finding the volume.
- Finds a missing dimension by dividing the volume by only one of the known lengths.
- Subtracts the known lengths from the volume instead of dividing.
- Divides the volume by the sum of the known lengths instead of their product.