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Memory Based GATE DA 2024 | Question: 46

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Consider two cones joined at a common circular base. If we cut a plane passing through the vertices of both cones, what type of shape will be formed by the intersection of the plane with the combined cones?

  1. Rhombus
  2. Triangle
  3. Hexagon
  4. Ellipse
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Answer: A. Rhombus

Explanation:

Let's first understand the case for a single cone. We know that a cone has a circular base with a curved surface. It possess a single vertex. Now we know that the slant height of a cone is observed to be constat when calculated from any side. If another cone is attached to this cone with a common circular base. This states that the other cone must possess a circular base with the same radius as that of the former. We assume that the cones shall have the same heights. If a cross-section is cut through this 3D figure passing through the 2 vertices, it would produce a 4 sided polygon with equal sides but with internal angle which could be 90 degree or not and equal opposite internal angles. Hence it would form a rhombus. Rhombus have these properties:

  • Have equal length sides.
  • Have internal angle which may or may not be 90 degree.
  • Have equal and opposite internal angles.
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