GATE DS&AI 2024 | GA Question: 10

Question

​​​​​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?

• A. A rhombus
• B. A triangle
• C. An ellipse
• D. A hexagon

Answer 1

When two identical right circular cones are assembled such that one is inverted over the other and they share a common circular base, the cross-section formed by a cutting plane passing through the vertices will result in an ellipse.

This is because the cross-section will intersect both cones at various angles, creating an elliptical shape. The widest part of the ellipse will correspond to the diameter of the circular base of the cones, and the length of the ellipse will vary depending on the angle of the cutting plane relative to the axes of the cones.

So, the correct answer is:

C. An ellipse

Comments

how ellipse or hexagon, can anyone explain?

I think the outer boundary will make a triangle!

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In the quest it is written vertices (plural) ie both includes in the cut .

It will form a rhombus

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Rhombus is correct 

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For visualization: http://www.shodor.org/interactivate/activities/CrossSectionFlyer/

or geogebra: https://www.geogebra.org/m/PzZfHugP#material/vwUxZJPR

Answer 2

Rhombus is the correct answer because there is a cross-section from the vertex of one cone to the vertex of another. See the figure below it satisfies all properties of Rhombus.

Answer 3

Answer: Rhombus

The correct answer would be RHOMBUS.

Here's how: