The formula for the surface area S of a rectangular solid with square bases is S=4wh+2w^2, where w is the side length of the bases and h is the height of the solid. Doubling each of the dimensions (w and h) will increase the surface area to how many times its original size?
the area of similar figures in 2D is proportional to the square of the
corresponding sides.
So
old area : new area = 1 : 2^2 = 1 : 4
so the surface area would be increased by a factor of 4.
of course you could just find the
new Area = 4(2w)(2h) + 2(2w)^2
= 16wh + 8w^2
= 4(4wh + 2w^2) = 4 times old original area