What line forms when a plane and a cylinder intersect?

Answer 1

When a plan intersects a volume, an area is formed by the intersection.

First, it depends on the angle at which the plan intersects the cyclinder. It if intersectes the cylinder perpendicular to the axis, a circle is formed.

If the plane intersects the cylinder at an angle, it will form an ellipse. This will be true until the plan is parallel with the axis of the cylinder. At that point, the surface will become a rectangle.

Answer 2

A circle is formed assuming the plane doesn't intersect the cylinder horizontally. If the cylinder is laying down and intersected in half by a plane then it wouldn't be a circle.

Answer 3

Take two spheres with radii equal to the radius of the
cylinder, and push them inside the cylinder from
opposite ends, until the spheres are tangent to the
plane at points F1 and F2. These spheres are also
tangent to the cylinder intself along two circles (belts)
C1 and C2, separated.by distance h.

Take any point A at the line formed by intersection
of the plane and the cylinder. The distance h1 from
A to the circle C1 is tangent to the first sphere.
The distance from A to F1 is also tangent to the
first sphere, and is therefore equal to h1:
h1 = |A C1| = |A F1|. Similarily h2 = |A C2| = |A F2|.

Since const = h = h1 + h2 = |A F1| + |A F2|,
the intersection of the plane and the cylinder is ellipse
which focii are F1 and F2. The same proof is good
true for conical sections too.

Answer 4

It depends if it intersects perpendicular to the axis of the cylinder (a circle) or if it is askew (an ellipse).

Answer 5

could be a retangle, a circle or a oval shape depending on the angle of intersection

Answer 6

a circle or an ellipse or one straight line or two straight parallel lines