You are given two options: (A) one chocolate cube of side 50 mm, (B) hundred chocolate cubes of side 10 mm. Which option gives you more chocolate?

Step-by-step solution

Idea: Compare volumes, not side lengths. A cube 5 times as long holds 5³ = 125 small cubes, not 5 or 100.

1. A: volume = 50 × 50 × 50 = 1,25,000 mm³.½ mark
2. B: volume = 100 × (10 × 10 × 10) = 100 × 1000 = 1,00,000 mm³.½ mark
3. 1,25,000 > 1,00,000, so option A gives more chocolate, by 25,000 mm³ (the big cube equals 125 small cubes).1 mark

Check: A 50 mm cube can be cut into 5 × 5 × 5 = 125 cubes of 10 mm, more than 100 ✓.

Answer to write in the exam

Common mistakes that cost marks

• Comparing sides (50 vs 10 × 100 = 1000) instead of volumes.
• Thinking 100 small pieces must be more than 1 big piece.

How this can come in the exam

Try one yourself

Which is more cheese: one 6 cm cube or thirty 2 cm cubes?

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