If you double the surface area of a box does it change?

Answer 1

Your question is a bit difficult to understand. Of course, if the box surface area is doubled, then the box is bigger. I suppose two valid questions are, if the sides are all increased by the same factor, what is this factor, and a second question is what is the new volume as compared to the initial one. If we look at the front face of the box, the area is height x width or A= H X W. So, if our length and with are multiplied by some factor, I will call X, to double the area, we have 2 A = H * X * W *X or X2*H*W =2A and if I substitute L*W for A, and cancel the A on each side, X2 = 2 or X = sqrt of 2. The same calculation can be made for the sides of the box, and you will see the factor is square root of 2 or 1.414. Now the second question is how much does the volume change. Since each side is larger by 1.414 and volume equals Height * width * depth, the volume increase by Factor = (2 1/2)3 = 2 3/2 or 2*sqrt(2) = 2*1.414 = 2.828 The box with double the surface area will have 2.828 more volume.