MTH 232
Section 9.3
Figures in Space
From 2-D to 3-D
• In the previous section we examined curves and
polygons in the plane (all the points in the plane
and its interior and exterior were coplanar).
• These figures had only two dimensions (for
example, a rectangle has length and width).
• In this section we expand our discussion to curves
and figures that cannot be contained within a flat
surface.
• In the absence of having actual models, these
three-dimensional figures are often drawn on a
two dimensional surface.
The Sphere
The Cylinder
The Cone
The Polyhedron
• A polyhedron is a simple closed surface
formed from planar polygonal regions.
• The polyhedron is to space what the polygon
is to the plane.
• Polyhedra have faces, vertices, and edges.
The Pyramid
The Prism
Euler’s Formula
• In 1752, Leonhard Euler discovered that the
number of faces (F), the number of vertices
(V), and the number of edges (E) are related to
one another:
V F  E2
Revised Homework
• 2 a, b, d ,e, f; 3; 12 a, b; 13; 17 (e-mail them to
me); 21; 23; 36; 37; 38