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

Hint:

When visualizing complex three-dimensional shapes intersected by planes, consider simplifying the shape into its symmetrical components and imagine how a plane would interact with these components at different angles.

Answer 1

The Correct Option is A

Step 1: Analyze the geometric setup. Two right circular cones are placed such that their vertices are opposite each other and they share a common base. The cutting plane passes through these vertices. Step 2: Determine the intersection shape. When a plane cuts through the vertices of the two cones, the intersection at the base of the cones is a straight line segment. Above and below this base, the sections through the cones are also straight lines if the cutting angle is the same from each vertex, forming a symmetrical shape. Step 3: Visualize the cross-section. The intersection of this plane with the two cones forms four linear segments, two from each cone, that meet at the vertices and at points on the base. This configuration resembles a rhombus - each side is equal in length due to the symmetry of the setup and the identical nature of the cones.