Question

If a brick has length, breadth and height in the ratio 1 : 2 : 3 and the total surface area of the brick is 792 ${\text{m}}^2$, then the volume of the brick is _______.

• A. $1,296{\text{m}}^3$
• B. $1,396{\text{m}}^3$
• C. $1,496{\text{m}}^3$
• D. $1,596{\text{m}}^3$

Answer 1

The correct option is A

$1,296{\text{m}}^3$

Given,
length(l) : breadth(b) : height(h) = 1:2:3
Total surface area = 792 sq. m

Let the length be $x\text{units}$.
Then, $b=2x\text{units}$ and $h=3x\text{units}$

$\text{Total surface area of cuboid}$
$=2(lb+bh+hl)$

$\Rightarrow 2(lb+bh+hl)=792$

$\Rightarrow 2(2x^2+6x^2+3x^2)=792$

$\Rightarrow 22x^2=792$

$\Rightarrow$ $x^2$ = $\frac{792}{22}=36$

$\Rightarrow x=6\text{m}$
(Since $x$ is the length and length is always positive.)

$\therefore l=6\text{m},b=12\text{m},h=18\text{m}$

Hence, volume = $lbh$
= $6\times 12\times 18$
= $1296{\text{m}}^3$