Question

Hello, i need help with question 5 :

«  suppose you have a cube with side =x and you would like to build its dual that fits inside of a cube. What will be the measure of a side of a dual in terms of X? Name the dual. » please !!

Answer 1

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,
`V = x^(3)` cubic units.

Now, volume of its dual is
`2V = 2x^(3)` 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
`V' = X^(3) = 2x^(3)`

⇒ X = x∛2 units. (Answer)