Lesson 2.6 Subsets of Space pp. 68-73

Objectives: 1. To identify a surface, closed surface, and solid. 2. To define sphere in terms of its center and radius. 3. To define cone and related terms. 4. To define cylinder and related terms. 5. To define prism and pyramid.

Definition A surface is a connected set of points in space having only the thickness of a point.

Definition A sphere is a surface in space consisting of the set of all points at a given distance from a given point.

Definition The center of a sphere is the given point. The radius of a sphere is a segment that connects a point of the sphere with the center.

sphere center radius

Definition A closed surface is a surface with a finite size that divides other points in space into an interior and an exterior.

Definition A solid is the union of a closed surface and its interior.

Definition A cone is the union of a region and all segments that connect the boundary of the region with a specific noncoplanar point.

A B k

A B k

Circular Cone C

Circular Cone C

Definition A cylinder is the union of two regions of the same size and shape in different parallel planes, and the set of all segments that join corresponding points on the boundaries of the region.

p1 p2

Definition A cylinder or a cone is circular if each base is a circle. A prism is a cylinder with polygonal regions as bases.

p1 p2

Definition A pyramid is a cone with a polygonal region as its base.

Right pyramid D L M O N

Oblique pyramid E T Q S R

Prism

Hexagonal Pyramid (regular) B C D E F

Homework pp. 71-73

►A. Exercises Identify each geometric figure with the most specific designation possible. 1.

►A. Exercises Identify each geometric figure with the most specific designation possible. 3.

►A. Exercises Identify each geometric figure with the most specific designation possible. 5.

►A. Exercises Identify each geometric figure with the most specific designation possible. 7.

►A. Exercises 9. Name the figure. Is it a surface? Use the diagram for exercises 9-11. 9. Name the figure. Is it a surface? M B A C D E

►A. Exercises 11. Name the lateral faces. What kind of polygon Use the diagram for exercises 9-11. 11. Name the lateral faces. What kind of polygon bounds each lateral face? M B A C D E

►A. Exercises 13. Name the bases. What kind of region are they? Use the figure for exercises 12-14. 13. Name the bases. What kind of region are they? A B C Q R P

►B. Exercises True/False. If the statement is false, explain why. 21. Every cone has a circular region for its base.

►B. Exercises True/False. If the statement is false, explain why. 23. Every pyramid has at least three lateral faces.

►B. Exercises True/False. If the statement is false, explain why. 25. All right pyramids are regular.

►C. Exercises 28. What is the intersection of a right circular cone and a plane parallel to the base of the cone?

►C. Exercises 29. If S is a sphere, C is the center of S, and P is a point on S, then is CP  S? How many points are in CP  S?

►C. Exercises 30. Do the radii of a sphere have equal lengths? Explain.

■ Cumulative Review True/False 31. A circle is a polygon.

■ Cumulative Review True/False 32. A hexagon is a region.

■ Cumulative Review True/False 33. A regular polygon is convex.

■ Cumulative Review True/False 34. An angle can consist of two opposite rays.

■ Cumulative Review True/False 35. The radii of a circle must have equal lengths.