How many small cubes with side 20 cm can be packed tight in a cubical box with side 2 m?

Step-by-step solution

Idea: Change to the same unit first. Then count how many fit along each edge, or divide the two volumes; both give the same answer because 20 divides 200 exactly.

1. Same units: side of box = 2 m = 200 cm.½ mark
2. Along each edge: 200 ÷ 20 = 10 small cubes.½ mark
3. Number of cubes = 10 × 10 × 10 = 1000. (Check by volumes: 200³ ÷ 20³ = 8 000 000 ÷ 8000 = 1000.)1 mark

Check: Volume of box = 8 000 000 cm³; volume of 1000 small cubes = 1000 × 8000 = 8 000 000 cm³ ✓.

Answer to write in the exam

Common mistakes that cost marks

• Not converting metres to centimetres and dividing 2 by 20.
• Dividing the sides only (200 ÷ 20 = 10) and forgetting to cube it.
• Converting 2 m³ wrongly as 200 cm³. 1 m³ = 100 × 100 × 100 = 1 000 000 cm³.

How this can come in the exam

Try one yourself

How many cubes of side 25 cm can be packed in a cubical box of side 1.5 m?

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