Volume of a Martini Glass

Question, how far up the side of a martini glass constitutes half the volume?

We can model the glass as a cone.
Volume of a cone:

If we add a term “” to denote the change.
The height affects the radius (r) linearly (similar triangles).
So and .

To find effect of halving the volume on the height:

Thus:

so:

So (if my maths is correct) you need to fill the glass to approximately 0.79 of the way up the side of the glass for half the volume.

..and who said maths wasn’t useful.