Cross Sections

Horizontal Plane

A plane parallel to the figures base

Cube

A 3D figure with 6 square sides. Think dice.

A square pyramid is sliced in such a way that the plane passes through all five faces of the pyramid, what is the resulting cross section?

Pentagon

Vertical Plane

A plane perpendicular to the base

A cone is sliced in such a way that the plane cuts in a direction parallel to the base, what is the resulting cross section?

Circle

A cylinder is sliced by a horizontal plane what is the resulting cross section?

Circle

The only cross section of a sphere. Varies in size but not in shape.

Circle

Which of the following is not a cross section of a rectangular prism? Rectangle, triangle, trapezoid, ellipse

Ellipse

A cone is sliced in such a say that the plane passes through the cylinder in a slanted direction without going through the base or the vertex, what is the resulting cross section?

Ellipse (0val)

A cylinder is sliced in such a way that the plane passes through the cylinder in a slanted direction without going through either base, what is the resulting cross section?

Ellipse (oval)

A right rectangular prism is sliced in a way such that the plane passes through all six faces of the prism, what is the resulting cross section?

Hexagon

What is the greatest number of sides that will result from a cross section of a rectangular prism?

6

Cross Section

A 2 dimension shape created by the intersection of a plane and a 3 dimensional figure. Specifically it is the area in which the plane and the figure meet.

Plane

A 2 dimensional figure with no boundaries. Think of a piece of paper, then extend all sides until you can't see them any more.

Cone

A 3D figure with a circular base, rounded sides that terminate at a vertex at the other end. Think ice cream cone.

Square Pyramid

A 3D figure with a square base and 4 triangular sides that terminate at a vertex. Think Egyptian pyramid.

Sphere

A 3D figure with no faces, just a continuous curved edge. Think an orange.

Cylinder

A 3D figure with parallel bases and a rounded edges. Think can of soup.

Rectangualr Prism

A 3D rectangle. Think a stick of butter.

How do you determine the shape of a cross section?

It will ALWAYS be the same shape as the figure to which it is parallel. IF the 3D figure has faces, the more faces the plane cuts through, the more sides the cross section will have.

A right rectangular prism is sliced in a way such that the plane passes through the prism at a slant. what is the resulting cross section?

Parelleogram

A right rectangular prism is sliced in a way such that the plane passes through five of the six faces of the prism,what is the resulting cross section?

Pentagon

A cylinder is sliced in such a way that the plane cuts in a direction perpendicular to the base,what is the resulting cross section?

Rectangle

A square pyramid is sliced by a horizontal plane, what is the resulting cross section?

Rectangle (of the same size as the 3D figure)

A right rectangular prism (with square base) is sliced such that the plane cuts in a direction parallel to the base, what is the resulting cross section?

Square

A right rectangular prism is sliced by a vertical plane, what is the resulting cross section?

Square or rectangle depending on dimensions of prism. EX. If it was a stick of butter the cross section would be a square.

What is the greatest number of sides a cross section can have?

The greatest number of sides a cross section can have is determined by the number of faces the 3D figure has. EX A triangular prism has 4 faces. The greatest number of sides that a resulting cross section can have is 4...so a resulting cross section could not be a pentagon, because it has 5 sides.

A square pyramid is sliced in such a way that the plane cuts in a direction perpendicular to the base but does not pass through the vertex, what is the resulting cross section?

Trapezoid

A cone is sliced by a vertical plane and passes through the vertex, what is the resulting cross section?

Triangle

A right rectangular prism is sliced in a way such that the plane passes through three intersecting edges, cutting off a corner of the prism, what is the resulting cross section?

Triangle

A square pyramid is sliced by a vertical plane and passes through the vertex, what is the resulting cross section?

Triangle

Can a cylinder produce a cross section that has 4 straight sides?

Yes, the perpendicular cross section of a cylinder is a rectangle (or a square depending on the cylinder's dimension.)