Similar solids: lengths scale by k, areas by k², volumes by k³. If k = 2, surface area is 4 times and volume is 8 times. Scale factor as a set is in scale factor.
Power matches the dimension
Linear, then square, then cube. Area and volume as a set are in area and volume. Area of a kite is a different leftover, in area of a kite.
The bottom line
k, k², k³. Do not scale a volume by k².
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