A scale factor k multiplies lengths. Area scales by k². Volume scales by k³. Double the edges and the area is four times, the volume eight. Similar triangles are the usual setup, in similar triangles.
Count the dimensions
One dimension: k. Two: k². Three: k³. Area and volume formulas are in area and volume. A pyramid volume still uses one-third, in volume of a pyramid.
The short list is in ACT Math formulas.
The bottom line
Lengths × k. Areas × k². Volumes × k³.
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