Question 747143
{{{highlight(800)}}}% 

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^2}}},
and the total surface area of the cube is {{{6s^2}}}.
 
If the length of the edge is tripled to {{{3s}}},
the surface area of each of the 6 faces of the cube is {{{(3s)^2=3^2s^2=9s^2}}},
and the total surface area of the cube is {{{6(9s^2)=54s^2}}}.
The absolute change is {{{54s^2-6s^2=48s^2}}}.
As a percentage of {{{6s^2}}}, that is {{{(48s^2/6s^2)*100=8*100=800}}}%
 
A factor of {{{3}}} change to a length, translates into a factor of {{{3^2=9}}} change to surface area, and it would translate into a factor of {{{3^3}}} 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^2}}} and the volume changes by a factor {{{k^3}}}.