My daughter's homework tonight has stumped me I'm embarrassed to say on how to come up with an "easy" solution.
The ratio between the volumes of 2 rectangular prisms is 5:4. The dimensions of the first prism are 3, 6, and 10. What are the dimensions of the second prism?
We can get the volume of the 2nd prism as 144 from the ratio. Now, because we need to multiply the number together 3 times, I can take the cube-root of the ratio (.8), which is ~.928 and multiply that against the original dimensions to get a volume of ~144. But yikes! There is no way 6th grade ratios should require that level of math. What am I missing except perhaps shaking my head in shame at the authors of this problem.
And the answer is - only the volumes are in ratio, not the dimensions. Dumb, dumb, dumb. I successfully made it much harder than it needed to be. 144x1x1, 12x12x1, etc.