Question

Three metallic cubes whose edges are 3 cm, 4 cm and 5 cm, are melted and recast into a single large cube. Find the edge of the new cube formed. [CBSE 2011]

Answer 1

$$\begin{gathered} \mathrm{We}\mathrm{have}, \\ \mathrm{Edges}\mathrm{of}\mathrm{the}\mathrm{cubes}:a_1=3\mathrm{cm},a_2=4\mathrm{cm}\mathrm{and}{a}_3=5\mathrm{cm} \\ \mathrm{Let}\mathrm{the}\mathrm{edge}\mathrm{of}\mathrm{the}\mathrm{new}\mathrm{cube}\mathrm{be}a. \\ \mathrm{Now}, \\ \mathrm{Volume}\mathrm{of}\mathrm{the}\mathrm{new}\mathrm{cube}={a_1}^3+{a_2}^3+{a_3}^3 \\ \Rightarrow a^3=3^3+4^3+5^3 \\ \Rightarrow a^3=27+64+125 \\ \Rightarrow a^3=216 \\ \Rightarrow a=\sqrt[3]{216} \\ \therefore a=6\mathrm{cm} \end{gathered}$$

So, the edge of the new cube so formed is 6 cm.