I have two right cones. One is a circular cone with height $h$ and half-angle $x$. EDIT: Both share the same apex and axis.
The other is an elliptical cone, with height $h$, minor half-angle $x$ and major half-angle $y$ where $y > x$.
Will the entire volume of the first (circular) cone always fit within the second?
This is for some software, and I need to know if I can make simplifying assumptions about the angles involved. If the circular always fits within the elliptical, than I can do a (much easier) circular cone check in some cases.
Maybe this just simplifies down to whether a circle of radius $r$ will always fit within an ellipse of minor axis $r$? (If so, then it's true, right?)
Please forgive any mistakes in terminology, this is a bit outside my knowledge base.