The surface area of a cubiod is3328 m²  . Its dimensions are in the ratio 4: 3:2 , then the volume of the cuboid is 

Surface Area of a cuboid = 3328 m³
$\begin{array}{l}2(\mathrm{lb}+\mathrm{bh}+\mathrm{hl})=3328\\ \mathrm{lb}+\mathrm{bh}+\mathrm{hl}=1664{\mathrm{m}}^2\to \left(1\right)\end{array}$
Given: $\mathrm{l}:\mathrm{b}:\mathrm{h}=4:3:2$
$\begin{array}{l}\therefore \mathrm{l}=4\mathrm{x},\mathrm{b}=3\mathrm{x},\mathrm{h}=2\mathrm{x}\\ \left(4\mathrm{x}\right)\left(3\mathrm{x}\right)+\left(3\mathrm{x}\right)\left(2\mathrm{x}\right)+\left(2\mathrm{x}\right)\left(4\mathrm{x}\right)=1664\\ 12{\mathrm{x}}^2+6{\mathrm{x}}^2+8{\mathrm{x}}^2=1664\\ 26{\mathrm{x}}^2=1664\\ {\mathrm{x}}^2=\frac{1664}{26}\\ {\mathrm{x}}^2=\frac{832}{13};{\mathrm{x}}^2=64\\ \mathrm{x}=\sqrt{64};\mathrm{x}=8\\ \mathrm{l}=4\mathrm{x}=4\left(8\right)=32\mathrm{m}\\ \mathrm{b}=3\mathrm{x}=3\left(8\right)=24\mathrm{m}\\ \mathrm{h}=2\mathrm{x}=2\left(8\right)=16\mathrm{m}\\ \text{ Volume of cuboid }=\mathrm{lbh}=32\times 24\times 16=12288{\mathrm{m}}^3\end{array}$