Given a cube with volume V, express its total surface area S in terms of V.

Step-by-step solution

Idea: Find the side from the volume, then put it in S = 6a².

1. V = a³ ⇒ a = ∛V = V^1/3.1 mark
2. S = 6a² = 6(V^1/3)² = 6V^2/3 = 6∛(V²).1 mark

Check: V = 8: a = 2, S = 24; 6 × 8^2/3 = 6 × 4 = 24 ✓.

Answer to write in the exam

Common mistakes that cost marks

• Writing S = 6V or S = 2V (forgetting the side is the cube root).
• Writing V^2/3 as 2V3.

How this can come in the exam

Try one yourself

Find S when V = 1000 cm³.

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