# Problem solving Conical glass

1. Sep 24, 2010

### skiing4free

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.

2. Sep 24, 2010

### Office_Shredder

Staff Emeritus
Why don't you explain how you got H:2h?

3. Sep 24, 2010

### skiing4free

Well the formula for a volume of a cone is:
V=1/3*pi*r^2*H.

V1 which is the volume of the full cone and V2 is the volume of the half full cone it is clear that V1/2=V2. I put the volume equations into this with the two differnt heights and when the constants are removed (pi, 1/3) you are left with H=2h. ahh but i have just seen how the radius would of course change... Now I think I am more confused

4. Sep 24, 2010

### Office_Shredder

Staff Emeritus
Can you find a relationship between what the radius and the height is going to be when you're at a certain height up the cone? (hint: think similar triangles)