I think the header summarises what I would like to do.
Regards
What is the apex angle measured against? Is it a vertical line which falls from the apex perpendicular to the base? (ie: bisecting the cone in the Z axis)
The volume of a cone is which for a circular base is
We can also "draw" a triangle with the angle made with the apex being . Since this is a right-angled triangle we can use trig:
Sub this expression for into
Rearrange for h:
As ever, you should always check I've not cocked up somewhere