Question

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

Answer 1

Let length of the given cuboid = 6x
Breadth of the given cuboid = 5x
Height of the given cuboid = 3x
Total surface area of the given cuboid
$=2(lb+bh+hl)=2(6x\times 5x+5x\times 3x+3x\times 6x)=(30x^2+15x^2+18x^2)=2\times 63x^2=126x^2$
But, we are given total surface area
$=504c{m}^2\therefore 126x^2=504\Rightarrow x^2=\frac{504}{126}\Rightarrow x^2=4\Rightarrow x^2=(2{)}^2\Rightarrow x=2cm$
$\therefore$ Length of the given cuboid = 6x
$=6\times 2cm=12cm$
Breadth of the given cuboid = 5x
$=5\times 2cm=10cm$
Height of the given cuboid = 3x
$=3\times 2cm=6cm$
Now, volume of the cuboid $=l\times b\times h$
$=12\times 10\times 6=720c{m}^3$