If the dimensions of a solid proportionally increase by a scale factor of , by what factor does the surface area increase?

There is not a scale factor provided.
rule of thumb

perimeter, length, etc. 
1- dimensions scale factor increases (scale factor)^1
think of answers ft, yd, etc.

area     
2-dimensional (l x w)  each dimension will increase by the scale factor. in this example, scale factor of 2(2l x 2w)  increase by 2^2 or 4
increased by (scale factor)^2,  think of answers given as ft^2, yd^2

volume
3-dimensional  (l x w x h), each dimension will increase by the scale factor.  in this example, scale factor of 2(2l x 2w x 2h) increased by 2^3 or 8
increases by (scale factor)^3, think of answers given as ft^3, yd^3

Hope this helps!!  Happy Studies.