Apply scale factors to length, area, and volume using k, k^2, and k^3 relationships.
Find the linear scale factor from a volume ratio of similar solids
Problem
Given the volume ratio \(\text{image}:\text{original}~=~27:1\), find the linear scale factor.
Big Picture
What this problem is really about
A volume ratio contains three copies of the linear scale factor, so it cannot be used directly as a length multiplier. We’ll keep the image-to-original direction, relate the ratio to the cube of the linear factor, undo that power with a cube root, and cube the recovered value as a check.
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