Question

Three cubes of iron whose edges are 6 cm, 8 cm and 10 cm, respectively are melted and formed into a single cube. Find the edge of the new cube formed.

Answer 1

$$\begin{gathered} \mathrm{We}\mathrm{have}, \\ \mathrm{Edges}\mathrm{of}\mathrm{the}\mathrm{cubes}:a_1=6\mathrm{cm},a_2=8\mathrm{cm}\mathrm{and}{a}_3=10\mathrm{cm} \\ \mathrm{Let}\mathrm{the}\mathrm{edge}\mathrm{of}\mathrm{the}\mathrm{new}\mathrm{cube}\mathrm{so}\mathrm{formed}\mathrm{be}a. \\ \mathrm{As}, \\ \mathrm{Volume}\mathrm{of}\mathrm{the}\mathrm{new}\mathrm{cube}\mathrm{so}\mathrm{formed}={a_1}^3+{a_2}^3+{a_3}^3 \\ \Rightarrow a^3=6^3+8^3+{10}^3 \\ \Rightarrow a^3=216+512+1000 \\ \Rightarrow a^3=1728 \\ \Rightarrow a=\sqrt[3]{1728} \\ \therefore a=12\mathrm{cm} \end{gathered}$$

So, the edge of the new cube so formed is 12 cm.