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Nanyang 2025 P6 Maths Prelim — Paper 2 Q12b Solution

Paper 2 · Q12b · 3 marks · Volume of Cube and Cuboid

Question

Lilian dipped the cube into a pail of paint. She then separated the cube back into the nine original wooden cuboids. Find the total unpainted area of the nine wooden cuboids.
Answer: 2592 cm^2

Worked solution

  1. Total surface area of all 9 cuboids: each cuboid is $18 \times 18 \times 2 = 648$, so each cuboid measures $18\text{ cm} \times 18\text{ cm} \times 2\text{ cm}$. Surface area of one cuboid $= 2(18 \times 18 + 18 \times 2 + 18 \times 2) = 2(324 + 36 + 36) = 792\text{ cm}^2$. Total for 9 cuboids $= 9 \times 792 = 7128\text{ cm}^2$. The painted area is the cube's outer surface $= 6 \times 18 \times 18 = 1944\text{ cm}^2$. But internal painted surfaces appear when separated
  2. total painted $= 7128 - 2592$. Unpainted area $= 2592\text{ cm}^2$.

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