Drag the 2D slider to change the location of the apex of the cone. The apex is in a plane parallel to the plane of the circular base.
All of these cones have the same volume, which for the bottom or top part is , where is the radius of the base and is the height.
The cone is only a right circular cone when the apex is directly over the center of the circle. However, for other positions its horizontal sections are still circles and planes still cut the cone in conic sections, so the box cuts it in parts of an ellipse, parabola, or hyperbola, depending on the angle.