Umm well heres the question describe what happens to a cube that the side dimensions that double or triple or quardruple and so on. So what happens to the surface area when you do it is there a specific scaling compairison
2007-01-29 16:21:55 · 5 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
Wow, deja vu. Anyway...
The volume of a cube is x^3 where "x" is the length of an edge. So when the edge length is increased by a factor of k, the volume is (kx)^3, which is (k^3)(x^3), or k^3 times the volume of the original cube. For example, if you take a cube and make a second cube whose edge lengths are double the size, the volume of the second cube will be 2^3 = 8 time the volume of the original cube.
The surface area of a cube is 6x^2, so if the length goes up by a factor of k, the new surface area is 6(kx)^2, or (k^2)*6x^2, which is k^2 times the original surface area. To use the cubes in the last example, the bigger one has a surface area that's 2^2 = 4 times that of the smaller one.
2007-01-29 16:32:46 · answer #1 · answered by Anonymous · 0⤊ 0⤋
The surface area is proportional to the square of the cube side. Specifically, the cube area A = 6*s^2, where s is the length of the side.
2007-01-30 00:27:09 · answer #2 · answered by Rick 5 · 0⤊ 0⤋
well, the surface area of one side of a cube is just length of a side squared, and there are 6 sides, so its just 6(X^2) When you double the side length, you quadruple the SA. when you triple, it will be 9x.
2007-01-30 00:29:04 · answer #3 · answered by Kyle M 6 · 0⤊ 0⤋
V = S^3
V2/V1 = S2^3/S1^3
If Sn = nS1,
Vn/V1 = n^3S1^3/S1^3
Vn/V1 = n^3
For surface area,
A = 6S^2
An/A1 = n^2
2007-01-30 00:30:37 · answer #4 · answered by Helmut 7 · 0⤊ 0⤋
it elevates to the same potence
2007-01-30 00:27:21 · answer #5 · answered by ? 5 · 0⤊ 1⤋