The cognac glass is described by its radial function
is the height when the glass is sitting on its base. In order to calculate the traditional measure of cognac (when the glass is placed on its side), we need the area enclosed by the chord
created by the cognac level
. That area is simply the area of its sector minus the area of its isosceles triangle. The volume is then equal to the integral over
from 0 to
(the brim of the glass), and depending on
, we must switch between the upper and lower areas enclosed by the chord. The popular measure of cognac (when the glass is placed standing up) is simply
is the point of maximum surface area.