Question

$2$cubes each of volume$64{\mathrm{cm}}^3$ are joined end to end. Find the surface area of the resulting cuboid.

Answer 1

Step 1:Find the side of cube.

$\begin{array}{rcl}\mathrm{Volume}\mathrm{of}\mathrm{cube}& =& 64{\mathrm{cm}}^3={\left(\mathrm{Side}\right)}^3\\ {\left(\mathrm{Side}\right)}^3& =& 64\\ \mathrm{Side}& =& {(64{\mathrm{cm}}^3)}^{\frac{1}{3}}\\ & =& {(2\times 2\times 2\times 2\times 2\times 2)}^{\frac{1}{3}}\\ & =& 2\times 2\\ \therefore \mathrm{Side}& =& 4\mathrm{cm}\end{array}$

Step 2:Find the surface area of the resulting cuboid.

Upon joining the two cubes the dimension of the cuboid will be,

Length$=8\mathrm{cm}$, breadth$=4\mathrm{cm}$, Height$=4\mathrm{cm}$

$\begin{array}{rcl}\mathrm{Surface}\mathrm{area}\mathrm{of}\mathrm{cuboid}& =& 2(\mathrm{lb}+\mathrm{bh}+\mathrm{hl})\\ & =& 2(8\times 4+4\times 4+4\times 8)\\ & =& 2(32+16+32)\\ & =& 2\left(80\right)\\ & =& 160{\mathrm{cm}}^2\end{array}$

Hence, the surface area of the resulting cuboid is$160{\mathrm{cm}}^2$.