Question

Length Ratio of a Cube/Cuboid

Answer 1

No such ratio exists. A cube of twice the side length has eight times the volume. However, you can say that the side length of a cube is the cube root of its volume.

If by "cuboid" you mean "rectangular prism", then the situation is even worse than for a cube, since there are infinitely many configurations with different measurements that all give the same volume.

Answer 2

You could use length and volume scale factor

Construct the most simple cuboid from your ratio, say 3x2x6 which will have a volume of 36 units^(3)

Then you know some scaled version of your constructed cuboid has volume 50 units^(3)

That means we scale the volume by 50/36=25/18 so each side length must be scaled by (25/18)^(1/3)

Work out each side length, and work out the product to check you get 50 back at the end