GATE 2024 CY – Question 10
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?
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Correct answer: (A) A rhombus
Explanation
Picture the double cone: two identical right circular cones glued base to base, with their axis vertical. The two vertices are at the top and the bottom.
**A plane through both vertices** contains the common axis. Such a plane cuts the double cone along a plane through its axis, so it passes through the diameter of the common base.
- The section of the upper cone is an **isosceles triangle** whose base is that diameter and whose other two sides are slant lines of the cone.
- The section of the lower cone is an identical isosceles triangle pointing downward on the same base.
Together the two triangles form a four-sided figure. All four sides are slant heights of the same cones, so **all four sides are equal**. A quadrilateral with four equal sides is a **rhombus** (option A).