Geometry

Question Analysis
This question involves the concept of similar solid figures, specifically cubes, and focuses on the relationship between the volumes of similar solids based on the ratio of their side lengths.
The main focus is understanding that for similar cubes (or any similar solids),  the ratio of volumes is equal to the cube of the ratio of their corresponding linear dimensions (in this case, side lengths).

Key Concept Explanation
If two similar solids have a scale factor (ratio of corresponding linear dimensions) of , the ratio of their volumes .
For cubes, since all side lengths are equal, the side - length ratio directly determines the volume ratio.

Step-by-Step Solution
Let the side - length ratio of the two cubes be , and the volume of the smaller cube cubic meters, and the volume of the larger cube be .
We know that .
Substitute the values:

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