Question

select the correct answer from the drop-down menu. a cylinder is sliced by a plane that is not parallel to the base and intersects only the lateral surface. the resulting cross section is a circle a parabola an ellipse a hyperbola

Explanation:

Step1: Recall Cylinder Cross - Section Rules

When a cylinder is sliced by a plane parallel to the base, the cross - section is a circle. When the plane is not parallel to the base and intersects only the lateral surface, we consider the nature of the intersection.
A cylinder can be thought of as a surface generated by moving a circle along a line (the axis of the cylinder). When a plane cuts the lateral surface of the cylinder at an angle (not parallel to the base), the intersection curve is an ellipse.

• A parabola is the cross - section of a cone when the plane is parallel to the side of the cone.
• A hyperbola is the cross - section of a cone when the plane is steeper than the side of the cone.
• A circle is the cross - section when the plane is parallel to the base of the cylinder.

Answer:

an ellipse