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 geometry of a cone: A cone is a three-dimensional shape with a circular base that tapers smoothly to a single point called the apex.
2. Visualize slicing the cone with a 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 slicing plane must be parallel to the base of the cone. This is because the base of the cone is circular, and a horizontal plane parallel to it will intersect the cone in a circular cross-section.
4. If the plane is slightly tilted, the intersection will form an ellipse, not a circle. The more the plane tilts, the more elongated the ellipse becomes.
5. If the plane is vertical or heavily tilted, the intersection will form other shapes, such as parabolas or hyperbolas, depending on the angle of the slice relative to the cone's axis.