Discussion
Visualize two identical right circular cones such that one is inverted over the other and they share a common circular base. If a cutting plane passes through the vertices of the assembled cones, what shape does the outer boundary of the resulting cross-section make?
Answer: A
The outline is a rhombus.
A plane through both apexes contains the common axis of the two cones. It cuts each cone in an isosceles triangle whose base is a diameter of the shared circular base. The two triangles share that diameter as a common side and point in opposite directions, so together they form a quadrilateral with all four sides equal to the slant height: a rhombus.
A single triangle would come from cutting one cone only. An ellipse arises when a plane cuts a cone without passing through its apex, and a hexagon cannot come from two cones.
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