Question

The length, breadth and height of a cuboid are in the ratio $6:5:3$. If the total surface area is $504$ $c{m}^2$,find its dimension. Also find the volume of the cuboid.

Answer 1

total surface area is $504c{m}^2$ The length, breadth, and height of a cuboid are in the ratio $6:5:3$

total surface area $=2(lb+bh+lh)$

$504$ = $2(30x^2+15x^2+18x^2)$

$504$ = $2$ x $63x^2$

$504$ = $126x^2$

$x^2$ = $\frac{504}{126}$ = $4$

$\therefore x=2cm$

Therefore,length= $6x$=$6$x$2$ = $12cm$

breadth = $5x$ =$5\left(2\right)$ =$10cm$

height = $3x=3\left(2\right)=6cm$

Volume of cuboid = area of the base x height = $l\times b\times h$ = $12$ x $10$ x $6$ = $720c{m}^3$