# Thread: Cubic

1. ## Cubic

Let C be a cube where the length of its diagonal is the same as its volume..what's the length of each side?

2. Well let the length of one side = x.

Volume = $x^3$

length of diagonal = $\sqrt{x^2 + x^2 + x^2}$ from Pythagoras' theorem.

Let them equal each other.

3. shouldn't be like square root (x2+x2) ...why for the diagonal..its' three times?

4. Originally Posted by franckherve1
shouldn't be like square root (x2+x2) ...why for the diagonal..its' three times?
The diagonal length of the base of the cube is $\sqrt{x^2 + x^2}$. Therefore ....

5. Well it's a cube isn't it? It's a three dimensional object. $\sqrt{x^2 + x^2}$ will give you the hypotenuse of two dimensions, but that is the diagonal along one face of the cube, from your question, I assumed you wanted the diagonal between opposing points of the cube, ie. front bottom left, to top right back.

in which case you will use the first hypotenuse and use Pythagoras' theorem with another edge piece to find the next hypotenuse (the answer you're searching for)

This is: $\sqrt{ \sqrt{x^2 + x^2}^2 + x^2} = \sqrt{x^2 + x^2 + x^2}$

6. and how to solve (square root)3x(squared)=X(cubic)

7. Well, $\sqrt{3x^2} = x^3$

square both sides, $3x^2 = x^6$

Then divide both sides by x squared $3 = x^4$

Then take a quartic root of both sides: $x = 3^{\frac{1}{4}}$

8. thanks so much!!