Cross Section Full Investigations

Edward Knote, Nov 14, 2016


  • 1. Cube Cross Sections Investigation
  • 2. Pyramid Cross Sections Investigation
  • 3. Cylinder Cross Sections Investigation
  • 4. Cone Cross Sections Investigation
  • 5. Sphere Cross Sections Investigation

1.

Cube Cross Sections Investigation

In the GeoGebra file below, use the tools to investigate the cross sections formed by cutting a plane through the three points located on the edges of the cube.
Investigation Directions:
Attempt to answer the questions below before playing with the file here.Then move the points I, K, and J around on the edges of the cube and investigate the cross sections.
Questions:
1. What is the shape of the cross section formed by slicing the cube above with the single plane through all three points J, K, and I? [br](Use the initial positions of points J, K, I, if you moved the points reset the GeoGebra file)
2. What are the different cross section shapes which can be formed by moving points J, K, and I anywhere along the edges of the cube, being sure the 3 points are not collinear?[br][br]
3. What is the least number of sides a cube cross-section shape can have? [br]
4. What is the greatest number of sides a cube cross section shape can have?
5. Can you slice cross section to form shapes with each of the numbers of sides in between the least and greatest number of sides? (Take pictures/screenshots of the above file as you investigate, showing each of the different cross sections you could find.)
Task PDF File:
– Edward Knote

2.

–

3.

–

4.

–

5.

–

Information