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GATE 2024 DA – Question 10

General Aptitude · Spatial Aptitude: Spatial Reasoning and Visualization · 2 marks · Multiple choice

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?

  1. A rhombus
  2. A triangle
  3. An ellipse
  4. A hexagon

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Show answer and explanation

Correct answer: (A) A rhombus

Explanation

A plane through both vertices contains the common axis of the cones. Its section of each cone is an isosceles triangle with the base as a diameter of the common circle. The two triangles share this base, one above and one below it, and together form a four-sided figure with all four sides equal (the slant height of the cones). That is a rhombus.