Question

The length, breadth and height of a cuboidal box are
$12x,10x$ and $6x$ respectively. If its total surface area is 2016 $c{m}^2$. Find its dimensions.

• A. $24\times 20\times 12$
• B. $8\times 10\times 12$
• C. $3\times 5\times 4$
• D. $12\times 10\times 6$

Answer 1

The correct option is A $24\times 20\times 12$

Given,
Total surface area of cuboid
= 2016 $c{m}^2$
length of cuboid (l)= $12x$.
breadth of cuboid (b)= $10x$.
height of cuboid (h)= $6x$.

We know that,
Total surface area of cuboid
= 2 (lb + bh + hl)
$\therefore$Total surface area of cuboid
=$2(12x\times 10x+10x\times 6x+6x\times 12x)$

But, we are given with total surface area of cuboid as 2016 $c{m}^2$.
$\therefore 2(12x\times 10x+10x\times 6x+6x\times 12x)$= 2016 $c{m}^2$
$\Rightarrow 504x^2=2016c{m}^2$
$\Rightarrow x^2=\frac{2016}{504}c{m}^2$
$\Rightarrow x=2cm$
So length = $12x=24cm$.
breadth = $10x=20cm$.
height = $6x=12cm$.