Question

Two cubes each of volume 27 cm³ are joined end to end to form a solid. Find the surface area of the resulting cuboid. [CBSE 2011, 14]

Answer 1

$$\begin{gathered} \mathrm{As},\mathrm{volume}\mathrm{of}\mathrm{a}\mathrm{cube}=27{\mathrm{cm}}^3 \\ \Rightarrow {\left(\mathrm{edge}\right)}^3=27 \\ \Rightarrow \mathrm{edge}=\sqrt[3]{27} \\ \Rightarrow \mathrm{edge}=3\mathrm{cm} \\ \mathrm{The}\mathrm{length}\mathrm{of}\mathrm{the}\mathrm{resulting}\mathrm{cuboid},l=3+3=6\mathrm{cm}, \\ \mathrm{its}\mathrm{breadth},b=3\mathrm{cm}\mathrm{and}\mathrm{its}\mathrm{height},h=3\mathrm{cm} \\ \mathrm{Now},\mathrm{the}\mathrm{surface}\mathrm{area}\mathrm{of}\mathrm{the}\mathrm{resulting}\mathrm{cuboid}=2\left(lb+bh+hl\right) \\ =2\left(6\times 3+3\times 3+3\times 6\right) \\ =2\left(18+9+18\right) \\ =2\times 45 \\ =90{\mathrm{cm}}^2 \end{gathered}$$