Two-Dimensional Slicing

Cross Section Study

 Describe the two-dimensional figures (cross sections) that result from slicing three-dimensional figures, as in plane sections of right rectangular prisms, right rectangular pyramids, cones, cylinders, and spheres. 

Cross Sections

• •What are cross sections?

  
  

  •What plane figures can I make by slicing a cube by planes?

  
  

  What about when I slice cones, prisms, cylinders, and pyramids instead of cubes

Multiple Choice

What is a cross section?

• 2- dimensional view of a 3-D shape

• 3-D view of a 2-dimensional shape

• 2- dimensional view of a 2-D shape

3 types of slices you will see

A left to right slice is parallel to the base.

An up and down slice is perpendicular to the base.

A diagonal slice is at an angle.

Horizontal (Parallel) to the base

This will always give you the shape of the base!

Vertical (Perpendicular)

This will always give you the shape of the face

Multiple Choice

If you slice a shape parallel to the base, what will the cross section be the shape of?

• face

• base

• stretched base

Cylinders

A parallel cross section gives you a circle

A perpendicular cross section gives you a rectangle

Multiple Choice

If you slice a shape perpendicular to the base (vertical), what will the shape always be?

• it will be considered as a face

• It will be considered the same shape as the base

• It will be considered an edge

• It will be considered a vertex

Multiple Choice

When you make a cut perpendicular to the base of a cone and starting at the vertex, the shape will be a ....

• cone

• rectangle

• square

• triangle

Rectangular Pyramids

• perpendicular (vertical) cuts give you a triangle

• parallel (horizontal) cuts give you a rectangle

Multiple Choice

What is the shape of the cross section that is parallel to the base of this figure?

• a circle

• cycloid

• parabola

• hyperbola

Triangular Prisms

Parallel cross sections give you the shape of the base, which is a triangle

Perpendicular cross sections to the base would give you a rectangle

Multiple Choice

What shape is the cross section that is parallel to it's base in this figure?

• pyramid

• prism

• square

• triangle

Cones

parallel=circle

perpendicular=triangle

Spheres

The cross section is a Circle no matter how you slice it.

Special

If you slice a square pyramid without going through the top (Vertex) you will get a trapezoid

Diagonal Slices (also known as Angled Slices)

will give you a stretched out base which is an Ellipse (also known as an oval)

Practice

Answer the questions in your head, then check your answers on the next slide.

Answers

Interactive Discovery

_{Copy and Paste the website into your URL. Then click on the various shapes to discover the different cross sections.}

_{https://www.geogebra.org/m/XCZwsytr}