Relationship Between Volume, Capacity and Mass
Primary 6 · Mathematics
Relationship Between Volume, Capacity and Mass
Lesson 3 of 5
15 min
Let's begin
Niyonzima is packing small cube-shaped boxes of chalk into a big carton for the school store. He wants to know how many will fit before he starts. The number of little cubes that fill the carton is its volume.
Volume is the amount of space an object takes up. We measure it in cubic units. A cube whose edges are all 1 cm long has a volume of 1 cubic centimetre (1 cm³). Bigger things are measured in cubic decimetres (dm³) or cubic metres (m³).
Think in layers. A carton is 20 cm long, 15 cm wide and 10 cm high.
Step 1 one layer on the bottom holds 20 × 15 = 300 one-centimetre cubes.
Step 2: there are 10 layers, one for each centimetre of height.
Step 3: volume = 300 × 10 = 3 000 cm³.
That is why volume of a cuboid = length × width × height.
For a cube, all three edges are equal: volume = side × side × side. A cube with 4 cm edges has volume 4 × 4 × 4 = 64 cm³.
A box has volume 120 cm³, length 6 cm and width 5 cm. What is its height?
Area of the base = 6 × 5 = 30 cm². Height = 120 ÷ 30 = 4 cm.
1 dm = 10 cm, so a 1 dm cube is 10 cubes long, 10 wide and 10 high:
1 dm³ = 10 × 10 × 10 = 1 000 cm³.
1 m = 100 cm, so 1 m³ = 100 × 100 × 100 = 1 000 000 cm³. Also 1 m³ = 1 000 dm³.
Worked examples
2.5 dm³ = 2.5 × 1 000 = 2 500 cm³. 3 m³ = 3 × 1 000 = 3 000 dm³.
Warning
A common mistake is to think 1 m³ = 100 cm³ because 1 m = 100 cm. But volume has three directions, so you multiply by 100 three times.
Take a hollow cube with inside edges of 10 cm. Its volume is 10 × 10 × 10 = 1 000 cm³. If you pour in a full 1 L bottle of water, it fills the cube exactly. So:
Worked example
How many litres does a box 10 cm × 10 cm × 20 cm hold?
Volume = 10 × 10 × 20 = 2 000 cm³ = 2 000 mL = 2 L.
Tip
For volume, count the cubes in one layer (length × width), then multiply by the number of layers (height). And remember: a 10 cm cube holds exactly 1 litre.
Answers
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Quick check
What is the volume of a cuboid 7 cm long, 4 cm wide and 5 cm high?
