Question

Find the volume of cuboid if its surface area is $208sqcm$ and the ratio of length, breadth and height is $2:3:4$.

Answer 1

Let length, breadth and height of cuboid be $2x,3x$ and $4x$ respectively.

Now,

Surface area of cuboid $=2(lb+bh+hl)=208{cm}^2\left(\text{Given}\right)$

$\therefore 2(2x\times 3x+3x\times 4x+4x\times 2x)=208$

$6x^2+12x^2+8x^2=104$

$\Rightarrow x^2=\frac{104}{26}$

$\Rightarrow x=\sqrt{4}=2$

As we know that,

Volume of cuboid

$=l\times b\times h=2x\times 3x\times 4x=24x^3=24\times 2^3=24\times 8=192{cm}^3$