Final answer:
The cross section formed by the intersection of a plane with the lateral surface of a cone can be a circle, ellipse, parabola, or hyperbola, with the exact shape depending on the angle of the plane.
Step-by-step explanation:
The cross section formed when a plane intersects with the lateral surface of a cone can be various conic sections such as a circle, ellipse, parabola, or hyperbola, depending on the angle of intersection.
If the intersection of the plane and the cone's lateral surface is parallel to the base of the cone, the cross section is a circle. The intersection here refers to the curve that is the result of the cutting plane and the cone's surface meeting.
This concept is fundamental in the study of conic sections in mathematics.
When a plane intersects a solid cone, the resulting shape is called a conic section. A circle is a special type of conic section that forms when the plane is parallel to the base of the cone.
The circle is the cross section of the cone. The lateral surface of the cone is the curved surface that connects the base to the vertex. It is shaped like a cone and has a circular cross section. The intersection of the circle and the lateral surface of the cone forms a curved figure.