5.11 Surface Area and Volume
The Polyhedron
I.SectionObjectives
- Identify polyhedral.
- Understand the properties of polyhedral.
- Use Euler’s formula to solve problems.
- Identify regular (Platonic) polyhedral.
II.ProblemSolvingActivity-UsingEuler
- During this activity, students are going to use Euler’s formula to determine the number of vertices, faces and
edges for the pyramid. - These pictures can be printed or if technology is available students can use a website to find the picture.
- Here is a picture of a pyramid with a rectangular base. This is Figure 11.01.01
- http://en.wikipedia.org/wiki/File:01_khafre_north.jpg
- Students need to create a three dimensional diagram of the pyramid.
- Then they can label the faces, vertices and edges of the pyramid.
- Finally, the students need to use Euler’s formula and demonstrate the accuracy of their answers.
- Extension is for students to draw the pyramid design to scale. This would involve more research as students
would need to search for the dimensions of the pyramid. - Then allow time for the students to share their work.
III.MeetingObjectives
- Students will identify polyhedrons.
- Students will understand the properties of polyhedra.
- Students will use Euler’s formula to solve problems.
- Students will demonstrate understanding through a diagram and presentation.
IV.NotesonAssessment
- Walk around as students are working on this assignment.
- Students may have difficulty picturing the rest of the pyramid given they can only see it from one perspective.
- Offer support by referring students back to the text.
- Another option is to provide students with a solid of a pyramid for them to work with.
- During presentations, listen for whether or not students have a grasp of Euler’s formula.
- Provide coaching/feedback as needed.
Representing Solids
I.SectionObjectives
5.11. Surface Area and Volume