the edges of a cuboid are in the ratio 1:2:3 and its volume is 1296cm.find its length,breadth and height?

Edges of cuboid are in the ratio of 1:2:3.
So, suppose the length, breadth and height of cuboid are x, 2x and 3x respectively.
Then, volume of cuboid = $x\times 2x\times 3x = 6x^3$
And the volume of cuboid given is 1296 ${\mathrm{cm}}^3$, so we have;
$$\begin{gathered} 6x^3 = 1296 \\ \Rightarrow x^3 = \frac{1296}{6} \\ \Rightarrow x^3 = 216 \\ \Rightarrow x^3 = 6^3 \\ x = 6 \end{gathered}$$
So, length of cuboid = 6 cm
Breadth of cuboid = 2$\times$ 6 = 12 cm
And height of cuboid = 3 $\times$ 6 = 18 cm