What happens to the surface area of a cube when it doubles?

Answer 1

I will rephrase your question: What happens to the surface area of a cube when the volume doubles. Ans. Surface area becomes 1.5876 times larger. Explanation: Let L = the length of the side of the original cube and h x L the length of the cube that is double the volume. Now: Vol= L^3 x 2 = (h x L)^3 or h = 2^(1/3) = 1.2599, so the length will be 1.2599 times larger. Surface area = 6 x L^2 for original cube and 6 x L^2 x 1.2599^2 for the cube with twice the volume. 1.2599^2 = 1.5876 If you are asking what happens to the surface area when the sides double, then the larger cube has surface area = 6 * 2^2 * L^2 , so 6 * 2^2 = 24. Each side is 4 times larger so the total surface area is 24 times larger.