This is a problem that my lecturer gave us in class and it has been bugging me ever since. I have been unsuccesful in finding or calculating a proper solution so I am hoping PF will be able to help... This is the Q: Let H be the height of a conical glass which is filled to a height h. Find the volume of the liquid in the glass as a proportion of the volume if the glass is full. Find the ratio h/H for which the glass is half full. To answer this question you must construct a mathematical model defining all the variables. This does not sound like a difficult question to solve but whenever I try to solve with simple conical volume equations I just get that the ratio is H:2h which is obviously not right. Any help would be greatly appreciated.