Question

Three cubes each of volume 125 cm³ are joined end-to-end to form a cuboid. Find the total surface area of cuboid.

Answer 1

Let the edge of each cube be a.

$$\begin{gathered} \mathrm{As}, \\ \mathrm{Volume}\mathrm{of}\mathrm{each}\mathrm{cube}=125{\mathrm{cm}}^3 \\ \Rightarrow a^3=125 \\ \Rightarrow a=\sqrt[3]{125} \\ \Rightarrow a=5\mathrm{cm} \\ \mathrm{So},\mathrm{the}\mathrm{length}\mathrm{of}\mathrm{the}\mathrm{cuboid},l=3a=3\times 5=15\mathrm{cm}, \\ \mathrm{the}\mathrm{breadth}\mathrm{of}\mathrm{the}\mathrm{cuboid},b=a=5\mathrm{cm}\mathrm{and} \\ \mathrm{the}\mathrm{height}\mathrm{of}\mathrm{the}\mathrm{cuboid},h=a=5\mathrm{cm} \\ \mathrm{Now}, \\ \mathrm{Total}\mathrm{surface}\mathrm{area}\mathrm{of}\mathrm{the}\mathrm{cuboid}=2\left(lb+bh+hl\right) \\ =2\left(15\times 5+5\times 5+5\times 15\right) \\ =2\left(75+25+75\right) \\ =2\times 175 \\ =350{\mathrm{cm}}^2 \end{gathered}$$

So, the total surface area of the cuboid so formed is 350 cm².