Use geometric methods to solve design problems under constraints such as cost, space, or ratios.
Separate length, area, and volume scale factors
Problem
Corresponding lengths are scaled by \(k~=~3\). State the length, area, and volume scale factors and classify the scaling as an enlargement or reduction.
Big Picture
What this problem is really about
A single scale factor acts once for each independent dimension. Keep the scaled-to-original direction fixed: linear measures use the factor itself, areas use its square, and volumes use its cube. After finding those three factors, compare the linear factor with one to classify the transformation as an enlargement or reduction.
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