Transcript Chapter 11: Surface Area & Volume

Chapter 11: Surface Area &
Volume
11.1
Space Figures & Cross Sections
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
Example 1
• How many vertices are there in the polyhedron?
• How many edges?
H
• How many faces?
F
G
D
E
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