 •  clin1066 posts in 1501 days #1 posted 08-17-2018 03:13 AM Not sure you said that right. I think that the cube of the factor only applies if you scale all 3 dimensions by the same factor. If you scale up a single dimension, you can simply multiply the volume by the scale factor to get the new volume. If you have a cylinder that is 3” tall and 3 inches in diameter, it has a volume of 21.2 cubic inches. If you double the height, it is the same as adding a second 3” tall 3” diameter cylinder on top so it simply doubles the volume to 42.4 because you changed only one dimension. If you triple the height only, the new volume is 3 times the original, not 27 times. If you double the diameter (but not the height), that is really the same as doubling 2 dimensions so the area of a cross section will increase by 4 times and volume of the scaled up cylinder is 84.8 which is the same as multiplying the original volume (21.2) by the square of the scale factor (4). - Lazyman Lazyman has it right. Though I had to re-read it a few times to understand it. I’ll restate in my own way. Assuming you have a known volume for some size of urn you already have. Call it Vold. The new volume is proportional to the change in height. Vnew is given by. Vnew = Vold x Kh Kh = Height new / Height old If you are changing the diameter (width), the volume changes by the square of the change in diameter. As Lazyman pointed out, you are effectively changing width and depth (2 dimensions). If you only changed one of these dimensions, it would become elliptical and not be circular. Vnew = Vold x Kd^2 = Vold x Kd x Kd (squaring Kd) Kd = Diameter new / Diameter old If you are changing both, it make no difference what order you apply these in. You can just say: Vnew = Vold x Kh x Kd^2 If both the height and width change by the same proportion ( K = Kh = Kd) then you have: Vnew = Vol x K^3 = Vold x K x K x K (K is cubed). Note: These of course are based on the interior dimension, not the exterior. -- Clin