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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

A cuboid A cuboid 5 cm 3 cm 4 cm
Volume of a cuboid Volume of a cuboid volume = length × width × height the rule volume = 5 × 4 × 3 put the numbers in volume = 20 × 3 multiply two at a time volume = 60 cm³ cubic centimetres

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.

Volume of a cube Volume of a cube volume = side × side × side all sides are equal volume = 4 × 4 × 4 a cube of side 4 cm volume = 64 cm³ the answer

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:

MeasureMultipliesUnit
Lengthone lengthcm
Areatwo lengthscm²
Volumethree lengthscm³

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

  1. What does one cubic centimetre look like?
  2. Find the volume of a cuboid 6 cm by 3 cm by 2 cm.
  3. Find the volume of a cube of side 5 cm.
  4. 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

  1. Cuboid volume = l x w x h; cube volume = s x s x s.
  2. Always include cm³ in the answer.
  3. All three measurements must be in the same unit.
  4. A cube is a cuboid where all three sides are equal.

Conclusion

Every volume calculation comes down to multiplying three dimensions together.

Check yourselfPractise Volume10 questions →Next in MathematicsCapacity