Martin S. answered • 04/05/20
Patient, Relaxed PhD Molecular Biologist for Science and Math Tutoring
Surface area is related to the square of dimensions. For example if you have a square with sides equal to one, and then double that to sides equal to two, the new square is four times as large in surface area. That would be 1 x 1 for the small square, and 2 x 2 for the large square, So for surface area ratios, use the square of how much bigger the large sides are compared to the small sides.
So, if you double all linear side dimensions, the ratio of big to small is 2. Take the square of that, which is 4, and that is how much more surface area the large prism has versus the small prism.
Let's take this a step further. What if all the sides were increased by a factor of three? What is the relationship between the increase of the side length and the increase of surface area?
Again, it is a relationship of the square of how much the sides increased. In this case the sides increased by a factor of 3, so the area increased by the square of that. 3 x 3 = 9 so the surface area increased by 9 fold.
What if we increased the dimensions by 10? It would have the same relationship, use the square of the increased side dimensions to find the increase of the surface area. That would be 10 x 10 = 100. So in that cast. making the sides 10 times as long makes the total surface area 100 times as great.
Hope this helps.
