SOLUTION: the percentage change in the surface area of a cube when each side is tripled is

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Question 747143: the percentage change in the surface area of a cube when each side is tripled is
Answer by KMST(5328) About Me  (Show Source):
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highlight%28800%29%
If the length of an edge of the cube is s,
the surface area of each of the 6 faces of the cube is s%5E2,
and the total surface area of the cube is 6s%5E2.

If the length of the edge is tripled to 3s,
the surface area of each of the 6 faces of the cube is %283s%29%5E2=3%5E2s%5E2=9s%5E2,
and the total surface area of the cube is 6%289s%5E2%29=54s%5E2.
The absolute change is 54s%5E2-6s%5E2=48s%5E2.
As a percentage of 6s%5E2, that is %2848s%5E2%2F6s%5E2%29%2A100=8%2A100=800%

A factor of 3 change to a length, translates into a factor of 3%5E2=9 change to surface area, and it would translate into a factor of 3%5E3 change to the volume.
The generalization is true for any scale-up (or scale down) of any solid, by any factor.
If you reproduce the shape changing every length by a factor k, the surface area changes by a factor k%5E2 and the volume changes by a factor k%5E3.