Question

which shape is a possible cross section of a cone?

ellipse
square
parallelogram
trapezoid

Explanation:

Analyze the cross sections of a cone

• A horizontal cross section parallel to the base of a cone is a circle.
• An angled cross section that cuts through all generators (sides) of the cone without intersecting the base is an ellipse.
• A vertical cross section passing through the apex is a triangle.
• A vertical cross section not passing through the apex is a hyperbola.

Evaluate the given options

• ellipse: Possible (by cutting the cone at an angle to the base).
• square: Impossible (a cone has a curved lateral surface and a circular base).
• parallelogram: Impossible (cannot be formed from a cone).
• trapezoid: Impossible (cannot be formed from a cone).

Answer:

• ellipse (Correct answer)
• square
• parallelogram
• trapezoid