1. Lesson 2.6
Subsets of Space pp

2. 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.

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

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

8. 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.

9. sphere
center
radius

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

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

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

15. A B k

16. A B k

17. Circular Cone C

18. Circular Cone C

19. 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.

20. p1 p2

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

22. p1 p2

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

24. Right pyramid D L M O N

25. Oblique pyramid E T Q S R

26. Prism

27. Hexagonal Pyramid (regular)B C D E F

28. Homework pp

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

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

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

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

33. ►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

34. ►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

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

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

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

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

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

40. ►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?

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

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

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

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

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

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