The surface area of a cubiod is $3328{\text{ m}}^2$ . Its dimensions are in the ratio $4:3:2$ , then the volume of the cuboid is

Surface Area of a cuboid $=3328m^2$

$2\left(lb+bh+hl\right)=3328$

$lb+bh+hl=1664{\text{ m}}^2\to \left(1\right)$

Given ,

$l:b:h=4:3:2$

$\therefore l=4x,b=3x,h=2x$

$\left(4x\right)\left(3x\right)+\left(3x\right)\left(2x\right)+\left(2x\right)\left(4x\right)=1664$

$12x^2+6x^2+8x^2=1664$

$26x^2=1664$

$x^2=\frac{1664}{26}$

$x^2=\frac{832}{13}$

$x^2=64$

$x=\sqrt{64}$

$x=8$

$l=4x=4\left(8\right)=32m$

$b=3x=3\left(8\right)=24m$

$h=2x=2\left(8\right)=16m$

Volume of cuboid $=lbh$

$=32\times 24\times 16$

$=12288{\text{ m}}^3$