Question

The dimensions of a cuboid are the ratio of $1:2:3$ and its total area is $88m^2$. Find the dimensions of the cuboid.

Answer 1

Ratio of dimensions of cuboid $=1:2:3$

$\frac{Length\left(l\right)}{Breadth\left(b\right)}=\frac{1}{2}$

$\Rightarrow b=2l$

$\frac{Breadth\left(b\right)}{Height\left(h\right)}=\frac{2}{3}$

$\Rightarrow 3b=2h$

$\frac{Length\left(l\right)}{Height\left(h\right)}=\frac{1}{3}$

$\Rightarrow 3l=h$

Total area$=88$m

Total surface area $=2(lb+bh+hl)$

$88=2\left[l\right(2l)+(2l\left)\right(3l)+(3l\left)l\right]$

$44=2l^2+6l^2+3l^2$

$11l^2=44$

$l=2$cm

$b=2l=4$cm; $h=3l=6$cm

Length$=2$cm

Breadth$=4$cm

Height$=6$cm.