Question

Three cubes of metal with edges 3 cm, 4 cm and 5 cm respectively are melted to form a single cube. Find the lateral surface area of the new cube formed.

Answer 1

Three cubes of metal with edges 3cm, 4cm and 5 cm are melted to form a single cube.

∴ Volume of the new cube = sum of the volumes the old cubes
$$\begin{gathered} =\left(3^3+4^3+5^3\right){\mathrm{cm}}^3 \\ =(27+64+125){\mathrm{cm}}^3=216{\mathrm{cm}}^3 \end{gathered}$$

Suppose the edge of the new cube = x cm
Then we have:
$$\begin{gathered} \mathrm{Then}216=x^3 \\ \Rightarrow x=\sqrt[3]{216}=6 \\ \mathrm{i}.\mathrm{e}.,\mathrm{the}\mathrm{edge}\mathrm{of}\mathrm{the}\mathrm{new}\mathrm{cube}\mathrm{is}6\mathrm{cm}. \end{gathered}$$

∴ Lateral surface area of the new cube = $4x^2{\mathrm{cm}}^2=4\times 6^2{\mathrm{cm}}^2=144{\mathrm{cm}}^2$