Chapter 11: Surface Area & Volume

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

2. Definitions • polyhedron: • 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 • p. 601 • 2-16 even, 36