How can you slice a vertically oriented 3D cone with a 2D plane to get a circle?

• A. Slice the cone with a horizontal plane.
• B. Slice the cone with a slightly tilted plane.
• C. Slice the cone with a heavily tilted plane.
• D. Slice the cone with a vertical plane.

Answer: (A)

Verified step by step guidance

1. Understand the shape of a 3D cone: A cone has a circular base and a pointed top, called the apex. When oriented vertically, the apex is directly above the center of the base.
2. Visualize slicing the cone with a 2D plane: A plane is a flat, two-dimensional surface that can intersect the cone in various ways depending on its orientation.
3. To obtain a circle, the plane must be parallel to the base of the cone. This means the plane should be horizontal, cutting through the cone at a level where the cross-section is a perfect circle.
4. Consider the position of the plane: If the plane is horizontal and cuts through the cone, it will create a circular cross-section. This is because the intersection of a plane parallel to the base of a cone is always a circle.
5. Recognize that other orientations of the plane, such as tilted or vertical, will result in different shapes like ellipses or parabolas, not circles.