ambiguity of half full

Besides the well known point-of-view issue with ‘half full’ (versus ‘half empty’), there is the issue that, while it is not ambiguous for a cylinder (drinking glass), it IS ambiguous for other containers, including the fairly common one of an inverted right circular cone. The task of filling a right circular cone halfway is ambiguous. If it means for us to fill it halfway up its height, then so doing will result in it containing 1/8 the volume of the cone, but if it means for us to fill it so that the volume is 1/2 of the volume of the cone, then we will need to fill it to about 71% of the height of the cone (exactly: square root of 2, over 2).
keywords: Mathematics, formula for the volume of a cone, calculation, water