Question

Two cubes each of volume $64c{m}^3$ are joined end to end. Find the surface area of the resulting cuboid.

Answer 1

Finding the surface area of the resulting cuboid:

The volume of cube $64c{m}^3$
Side of cube $\sqrt[3]{64}=4cm$ $\left[\because \mathrm{side}={\left(\mathrm{Volume}\right)}^{\frac{1}{3}}\right]$

Length of resulting cuboid $4+4=8cm$

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

Therefore, the surface area of the resulting cuboid is $\mathbf{160}\mathbf{}{\mathbf{cm}}^{\mathbf{2}}$