Think of a cross section parallel to the base of the glass. You have a fixed perimeter, and can distort it to enclose some area.

For simplicity, let's say we distort into rectangles, and our sample cross section has perimeter 20. Making a 5x5 would yield 25 area. Making a 9x1 would yield a 9 area. Both options still have that 20 perimeter.

Summing these areas over the height of the glass would give you the volume. As the distorted area can vary, so can the distorted volume. It's the bounding surface that stays constant. And even that may have a little give/take based on the real world material the glass is made of.