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

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

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

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

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

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

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

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.

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

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

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

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

Homework p. 601 2-16 even, 36