14.3 Geometry in Three Dimensions

Simple Closed Surfaces

** A simple closed surface has ** one interior**,

Ex. Sphere See Figure

a-d are simple closed surfaces e, f are not simple closed surfaces

Def. __Sphere__—the set of all points
at a given distance from a given point, the center.

Def. __Solid__—the set of all points on
a simple closed surface with all interior points.

Def. __Polyhedron__—a simple closed surface made up of
polygonal regions, or faces.

**PRISMS**

Def. __Prism__—a polyhedron in which two congruent faces
lie in parallel planes and the other faces are bounded by parallelograms.

**faces other than the bases are the __lateral faces__**

**if the lateral faces of a prism are all bounded by rectangles, then the prism is a right prism; if not, it is an oblique prism.**

**PYRAMIDS**

Def. __Pyramid__—a polyhedron determined by a polygon and
a point not in the plane of the polygon.

Base----polygonal region

Point---apex

Faces other than the base---lateral faces

Figure —triangle, square, pentagonal

**CYLINDERS AND CONES**

Def. __Cylinder__—a simple closed
surface that is not a polyhedron.

Ex’s: circular cylinder—when the base is a circle

right cylinder—when the line segment forming a cylinder is perpendicular to the base.

Def. __Cone__—a simple closed surface
that is not a polyhedron, with a vertex.

*vertex

*altitude

Ex’s right circular cone

Oblique circular cone