Discussion
Three metallic solid cubes of sides 8 cm, 6 cm and 10 cm are melted to form a single solid cube. The side of the new cube so formed is :
Answer: D
The side of the new cube is 12 cm.
Melting keeps the total volume the same, so add the three volumes and take the cube root.
\[ \begin{aligned} V &= 8^{3} + 6^{3} + 10^{3} \\ &= 512 + 216 + 1000 = 1728 \\ \text{side} &= \sqrt[3]{1728} = 12 \text{ cm} \end{aligned} \]
The common mistake is adding the sides, \(8 + 6 + 10 = 24\) cm, which assumes length is conserved instead of volume. 20 cm and 18 cm are similar guesses that do not cube to 1728.
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