Question

Two cubes, each of volume 64 cm³, are joined end to end. Find the total surface area of the resulting cuboid.

Answer 1

Volume of the cube = a³

Therefore,
$$\begin{gathered} a^3=64 \\ \Rightarrow a^3={\left(4\right)}^3 \\ \Rightarrow a=4\text{cm} \end{gathered}$$

Each side of the cube = 4 cm

Then,
Length of the cuboid $\Rightarrow \left(2\times 4\right)\text{cm=8 cm}$
Breadth of the cuboid = 4 cm
Height of the cuboid = 4 cm

Total surface area of the cuboid $=2\left(lb+bh+lh\right)$
$$\begin{gathered} =2\left[\left(8\times 4\right)+\left(4\times 4\right)+\left(8\times 4\right)\right]{\text{cm}}^2 \\ =\left(2\times 80\right){\text{cm}}^2 \\ =160{\text{cm}}^2 \end{gathered}$$