Question

The dimension of rectangular parallelopiped are in the ratio $6:5:4$ and its total surface area is $33300$ square meters. Find its volume.

Answer 1

Let length, breadth, and height of a cuboid are $6x$, $5x$, and $4x$ respectively.

Its total surface area;

$=2(lb+bh+hl)$

$=2(6x\times 5x+5x\times 4x+4x\times 6x)$

$=2(30\times x^2+20\times x^2+24\times x^2)$

$=2\times 74\times x^2$

$=148\times x^2$

But it is given that total surface area$=33300sq.m$

i.e. $148\times x^2=33300$

$\Rightarrow x^2=\frac{33300}{148}$

$\Rightarrow x^2=225m^2$

$\Rightarrow x=\sqrt{225}$

$\Rightarrow x=15m$

Dimensions of cuboid are;

$6x=6\times 15=90m$

$5x=5\times 15=75m$

and $4x=4\times 15=60m$

Volume of cuboid$=90\times 75\times 60$ cubic metres$=405000$ cubic metres.