1. Chapter 11: Surface Area & Volume
11.1
Space Figures & Cross Sections

2. Definitions polyhedron: face edge vertex
three-dimensional figure whose surfaces are polygons
face
each surface of the polyhedron
edge
segment formed by the intersection of two faces
vertex
point where three or more edges intersect

3. Example 1 How many vertices are there in the polyhedron?
How many edges?
How many faces?

4. Euler’s Formula
The numbers of faces (F), vertices (V), and edges (E) of a polyhedron are related by the formula F + V = E + 2.
For two-dimensional (like with a net): F + V = E + 1

5. Example 2
Use Euler’s Formula to find the number of vertices in the polyhedron:

6. Example 2A
Use Euler’s Formula to find the number of edges on a polyhedron with eight triangular faces.

7. Example 3
Verify Euler’s Formula for a two-dimensional net of the solid in Example 2.

8. Example 3a Verify Euler’s formula for a trapezoidal prism.
Draw a net for the prism.
Verify Euler’s formula for your two-dimensional net.

9. Cross Section intersection of a solid figure and a plane
think “cutting” the solid figure
MRI’s or CT scans work in this way!

10. Example 4 Describe each cross section:
a box, cut through the middle with a plane
a triangular prism, cut through the middle with a plane

11. Example 5
Draw and describe a cross section formed by a vertical plane intersecting the front and right faces of the cube.

12. Example 5a
Draw and describe the cross section formed by a horizontal plane intersecting the left and right faces of the cube.

13. Homework
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2-16 even, 36