Discussion
Three cubes whose edges are 8 cm, 6 cm and 1 cm respectively are melted without any loss of metal into a single cube. What is the edge of cube?
Answer: B
The edge of the new cube is 9 cm.
No metal is lost, so the new volume is the sum of the three volumes:
\[ \begin{aligned} V &= 8^{3} + 6^{3} + 1^{3} \\ &= 512 + 216 + 1 = 729 \\ a &= \sqrt[3]{729} = 9\ \text{cm} \end{aligned} \]
Adding the edges (15 cm) is the trap; volumes add, edges do not. 8 cm is the largest original cube and must be exceeded, while 10 cm and 7 cm give volumes of 1000 and 343, not 729.
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