To determine which measurements need to be equal in all three solids for a specific ratio of volumes to hold true, it's essential to consider the properties of the solids involved. The relationship between their dimensions (like radius and height) directly influences their volumes.
If the solids in question are, for example, three different shapes like a cylinder, a cone, and a sphere, the volume is affected by both height and radius (and the specific formulas for volume).
Therefore, the most appropriate choice based on volume relationships is:
The radius and the height.
Having the radius and height equal will help ensure the volumes of the solids can relate in a consistent ratio.