In order for 2D shapes to be similar, the dimensions must be similar. If two rectangles are similar at a ratio of 1:4, then the length and the width are each at a ratio of 1:4.
Buuuuuut, when we multiply to find the area, the ratio of the area is 1:16.
Let's say we have one rectangle that's 3 x 5 and another that's 12 x 20. The two areas are 15 and 240, and 240/15 = 16, right?
So, because we have similar bottles, again, the 2D dimensions are similar, maning the height is 1:4, but since we multiply the area of the base by the height to get the volume, the ratio of the volume is 1:16.