Answer:[tex]31.17\ in[/tex]
Step-by-step explanation:
Given
Edge length of cube is [tex]a=18\ in.[/tex]
From the figure, distance between the opposite corner of the tank is
[tex]\Rightarrow (xy)^2+(xz)^2=(yz)^2\\\Rightarrow a^2+(a\sqrt{2})^2=(yz)^2\\\Rightarrow (yz)^2=3a^2\\\Rightarrow (yz)^2=3\times (18)^2\\\Rightarrow yz=18\sqrt{3}\\\Rightarrow yz=31.17\ in.[/tex]
Therefore, the length of the opposite corners is [tex]31.17\ in[/tex]
