llaffer
If the ratio of lengths of similar shapes is x:y, then the ratio of their surface areas would be the square: x²/y² and the ratio of their volumes would be the cube: x³/y³
You are told that the surface area of one cube is twice the other, so:
2:1
We'll need to get the square root of this ratio to get the ratio of the lengths:
√(2):1
And then cube of this ratio to get the ratio of the volume:
√(2³):1 or 2√(2):1