A metal solid cube of edge 24\text{ cm} is melted and made into three small cubes. If the edges of two small cubes are 12\text{ cm} and 16\text{ cm}, then what is the surface area of the third small cube?
- A. 1200\text{ cm}^2
- B. 1800\text{ cm}^2
- C. 2400\text{ cm}^2 ✓
- D. 3600\text{ cm}^2
Correct Answer: C. 2400\text{ cm}^2
Explanation
Volume is conserved: 24^3 = 12^3 + 16^3 + a^3 \implies 13824 = 1728 + 4096 + a^3 \implies a^3 = 8000, so the edge of the third cube a = 20\text{ cm}. Its surface area is 6a^2 = 6(20^2) = 2400\text{ cm}^2.
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