Volume
Measurement · Volume
CBC Grade 5 Mathematics — Volume
Lesson Objectives
By the end of this topic, a learner should be able to:
- Identify the cubic centimetre as a unit for measuring volume
- Work out the volume of a cuboid using length x width x height
- Work out the volume of a cube using side x side x side
- Appreciate the use of volume in everyday situations
Volume
Volume is the space a solid object takes up. A brick has volume. A box has volume. A flat sheet of paper has almost none.
a) The cubic centimetre
We measure volume in cubic centimetres, written cm³.
One cubic centimetre is a small cube measuring 1 cm along every edge.
Picture filling a box with these little cubes and counting them. That count is the volume.
b) Counting cubes
Take a box 5 cm long, 4 cm wide and 3 cm high.
Fill the bottom layer. It takes 5 × 4 = 20 cubes.
There are 3 layers. So altogether there are 20 × 3 = 60 cubes.
c) Volume of a cuboid
The rule is volume = length × width × height.
Multiply two of them first, then multiply by the third. The order does not matter.
All three measurements must be in the same unit.
d) Volume of a cube
A cube has all its edges the same length.
So the rule is volume = side × side × side.
A cube of side 4 cm has a volume of 64 cm³.
e) Cubic units, every time
Volume answers always end in cm³.
The small 3 tells you three lengths were multiplied together.
Compare the three:
| Measure | Multiplies | Unit |
|---|---|---|
| Length | one length | cm |
| Area | two lengths | cm² |
| Volume | three lengths | cm³ |
Looking at the small number tells you which one you have found.
f) Where this is used
Filling a box with goods. Working out how much water a tank holds. Measuring soil for a planting bag. Packing a lorry.
:::checkpoint Check yourself
- What does one cubic centimetre look like?
- Find the volume of a cuboid 6 cm by 3 cm by 2 cm.
- Find the volume of a cube of side 5 cm.
- What units does volume use? :::
Definitions
- Volume — the amount of space a solid object takes up.
- Cubic centimetre (cm³) — a cube measuring 1cm on every edge.
- Cuboid — a solid shape with six rectangular faces.
Must Remember
- Cuboid volume = l x w x h; cube volume = s x s x s.
- Always include cm³ in the answer.
- All three measurements must be in the same unit.
- A cube is a cuboid where all three sides are equal.
Conclusion
Every volume calculation comes down to multiplying three dimensions together.