Discussion
Three metal cubes with edges 6 cm, 8 cm and 10 cm respectively are melted together and formed into a single cube. Find the side of the resulting cube.
Answer: A
The side of the new cube is 12 cm.
Melting and recasting keeps the total volume:
\[ \begin{aligned} 6^{3} + 8^{3} + 10^{3} &= 216 + 512 + 1000 \\ &= 1728 = 12^{3} \end{aligned} \]
Adding the edges (6 + 8 + 10 = 24) is the trap that gives the 24 option; volumes add, edges do not. 11 and 13 cm give volumes of 1331 and 2197 cm3.
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