Question

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?

Answer 1

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