Answer:
Measurements of each side of the dual in terms of x will be x∛2 units.
Step-by-step explanation:
If the side of the original cube is x units, then its volume will be, [tex] V = x^{3}[/tex] cubic units.
Now, volume of its dual is [tex] 2V = 2x^{3}[/tex] cubic units.
Therefore, if I would like to build the dual of the original cube that fits inside another cube, then the measurement of each side of this dual cube is X units.
So, volume of the dual cube [tex]V' = X^{3} = 2x^{3}[/tex]
⇒ X = x∛2 units. (Answer)
