Question

Two cubes each of volume 125 cm³ are joined end to end to form a solid. Find the surface area of the resulting cuboid. [CBSE 2013C]

Answer 1

$$\begin{gathered} \mathrm{Let}\mathrm{the}\mathrm{edge}\mathrm{of}\mathrm{the}\mathrm{cube}\mathrm{be}a. \\ \mathrm{As}, \\ \mathrm{Volume}\mathrm{of}\mathrm{the}\mathrm{cube}=125{\mathrm{cm}}^3 \\ \Rightarrow a^3=125 \\ \Rightarrow a=\sqrt[3]{125} \\ \Rightarrow a=5\mathrm{cm} \\ \mathrm{So}, \\ \mathrm{Length}\mathrm{of}\mathrm{the}\mathrm{resulting}\mathrm{cuboid},l=2\times 5=10\mathrm{cm}, \\ \mathrm{Breadth}\mathrm{of}\mathrm{the}\mathrm{resulting}\mathrm{cuboid},b=5\mathrm{cm}\mathrm{and} \\ \mathrm{Height}\mathrm{of}\mathrm{the}\mathrm{resulting}\mathrm{cuboid},h=5\mathrm{cm} \\ \mathrm{Now}, \\ \mathrm{Surface}\mathrm{area}\mathrm{of}\mathrm{the}\mathrm{resulting}\mathrm{cuboid}=2\left(lb+bh+hl\right) \\ =2\times \left(10\times 5+5\times 5+5\times 10\right) \\ =2\times \left(50+25+50\right) \\ =2\times 125 \\ =250{\mathrm{cm}}^2 \end{gathered}$$

So, the surface area of the resulting cuboid is 250 cm².