A(n) _____ is produced when you slice a cone with a plane that is parallel to the base of the cone.A.circleB.parabolaC.hyperbolaD.ellipse

To solve this question, we need to analyze the geometric properties of conic sections.

1. Break Down the Problem

We are determining what shape is formed when a cone is sliced by a plane parallel to its base. The possible answers provided are:

• A. Circle
• B. Parabola
• C. Hyperbola
• D. Ellipse

2. Relevant Concepts

In geometry, a conic section refers to the different shapes that can be formed by slicing a cone in various ways:

• A circle is formed when the slice is parallel to the base and the cone is right circular.
• An ellipse is formed when the slice is made at an angle, but not steep enough to form a parabola.
• A parabola occurs when the slicing plane is parallel to a slant height of the cone.
• A hyperbola results from slicing through both nappes of the cone.

3. Analysis and Detail

When a cone is sliced by a plane parallel to the base, the distance from the vertex to the base remains constant, resulting in a circular cross-section regardless of the height at which the slice is made.

4. Verify and Summarize

Since the cutting plane is explicitly parallel to the base of the cone, the section obtained will always be circular in shape.

Final Answer

The answer is A. Circle.