Question

Describe different ways in which a plane might Intersect the cylinder, and the cross section that results. If the plane intersects the cylinder horizontally, the cross section is (select) If the plane intersects the cylinder slanted between horizontal and vertical, the cross section is (select) If the plane intersects the cylinder vertically through the cylinder, the cross section is (select) If the plane intersects the cylinder vertically along an edge of the cylinder, the cross section is (select)

Answer 1

When a plane intersects a cylinder, the resulting cross section can be a circle, ellipse, rectangle, or parabola depending on the orientation of the plane.

Step-by-step explanation:

When a plane intersects a cylinder, the resulting cross section can take different shapes depending on the orientation of the plane. Here are the different possibilities:

1. If the plane intersects the cylinder horizontally, the cross section is a circle. This is similar to cutting a cylinder with a knife parallel to its base.
2. If the plane intersects the cylinder slanted between horizontal and vertical, the cross section is an ellipse. This shape looks stretched or compressed.
3. If the plane intersects the cylinder vertically through the cylinder, the cross section is a rectangle. This is similar to cutting the cylinder straight down the middle, creating two halves.
4. If the plane intersects the cylinder vertically along an edge of the cylinder, the cross section is a parabola. This shape looks like a curved line.

Answer 2

If we intersect a plane with the cylinder horizontally, the cross section is a circle.

If we intersect a plane with the cylinder slanted, the cross section is an oval.

If we intersect a plane with the cylinder vertically through the cylinder, the cross section is a rectangle.

And if we intersect a plane with the cylinder vertically along an edge, the cross section is a line.