1. Geometric Solids and Surface Area
Geometry
Regular Program SY
Sources:
Discovering Geometry (2008) by Michael Serra
Geometry (2007) by Ron Larson

2. These DO NOT have CURVED surfaces.
The Geometric Solids
These DO NOT have CURVED surfaces.
Observe that these have CURVED surfaces.

3. Observe that these also have CURVED surfaces.
The Geometric Solids
Observe that these also have CURVED surfaces.

4. FACE – each polygonal surface
The Geometric Solids
A solid formed by polygons that enclose a single region of space is called a POLYHEDRON (pl. polyhedra)
FACE – each polygonal surface
EDGE – segment where 2 polygons intersect
VERTEX – point where 3 or more edges intersect

5. Classification of Polyhedra
Polyhedra are classified
according to the number of faces
6 faces
7 faces
10 faces

6. Classification of Polyhedra
How many faces does a
tetrahedron have ?
REGULAR POLYHEDRON – a polygon whose faces are congruent regular polygons

7. Which are polyhedra?

8. Has 2 parallel & congruent bases PRISM
Other faces are LATERAL faces, which are parallelograms
LATERAL EDGES
base

9. - classified according to base
PRISM
- classified according to base

10. Lateral faces are rectangles. Lateral faces: NOT rectangles.
RIGHT vs OBLIQUE
PRISM
Lateral faces are rectangles.
Lateral faces: NOT rectangles.

11. Has 2 parallel & congruent bases
CYLINDER
base
LATERAL face
base

12. Axis is perpendicular to the circular base. Axis is NOT perpendicular
RIGHT vs OBLIQUE
CYLINDER
Axis is perpendicular to the circular base.
Axis is NOT perpendicular
to the circular base.

13. Has only 1 base
PYRAMID
Vertex of pyramid
LATERAL faces
are triangles.
LATERAL EDGES
base

14. The slant height is the height of a triangular face.
In a pyramid, there is a
“slant height”.
PYRAMID
The slant height is the height of a triangular face.

15. - classified according to base PYRAMID
Which of these pyramids are right? Oblique?

16. Has only 1 base
CONE
Vertex of cone
Slant height
Height of cone
LATERAL face
base

17. RIGHT vs OBLIQUE
CONE

18. SPHERE

19. HEMISPHERE: Half a sphere PLUS the circular base
The circle that encloses the base is the GREAT CIRCLE.
If a plane cuts a sphere along the center, then the plane contains the great circle.
If you were to slice a pingpong ball, where do you slice it to get the largest circular cross-section?
Is the equator In a globe a great circle?

20. What solid is illustrated? Be specific.
Exercises

21. What solid is illustrated? Be specific.
Exercises

22. What solid is illustrated? Be specific.
Exercises

23. What solid is illustrated? Be specific. Exercises
Conservatories in Edmonton, Canada
Containers in an ice
cream plant in
Burlington, Vermont

24. What solid is illustrated? Be specific. Exercises
A bag of oranges

25. The surface area of any given solid is the
What is SURFACE AREA?
The surface area of any given solid is the
SUM of the areas of ALL EXPOSED and TANGIBLE faces that enclose the solid.

26. STRATEGY! Draw each face. Get area of each face. Add all areas.
SURFACE AREA
Example A:
STRATEGY!
Draw each face.
Get area of each face.
Add all areas.

27. SURFACE AREA
Solution:

28. SURFACE AREA
Solution:

29. STRATEGY! Draw each face. Get area of each face. Add all areas.
SURFACE AREA
Example B:
STRATEGY!
Draw each face.
Get area of each face.
Add all areas.

30. SURFACE AREA
Solution:

31. SURFACE AREA
Solution:

32. How do we get the surface area of a pyramid?
Example C:
How do we get the surface area of a pyramid?
STRATEGY!
Draw each face.
Get area of each face.
Add all areas.
Get area of TRIANGLES and the area of the BASE!

33. The pyramid has a square base with perimeter 48, and a height of 8 cm.
SURFACE AREA
Example C:
The pyramid has a square base with perimeter 48, and a height of 8 cm.
slant height 8 10 6 12 12
Total SA = 4 Congruent Triangular Faces + 1 square 12 12 10 12

34. SURFACE AREA
Example D:
Is there a formula to get the surface area of a right pyramid with a regular base?
Solution:
Lateral Area + Base Area

35. SURFACE AREA

36. How about the surface area of a cone?
Example D:
How about the surface area of a cone?
Lateral face is a sector!

37. SURFACE AREA

38. PRISM CYLINDER PYRAMID CONE
SURFACE AREA
Total SA =
Lateral Area +
Base Area
PRISM +
CYLINDER
PYRAMID
CONE

39. Exercises on Surface Area Solve for the surface area of each given solid

40. Exercises on Surface Area Solve for the surface area of each given solid

41. Exercises on Surface Area Solve for the surface area of each given solid

42. Exercises on Surface Area Solve for the surface area of each given solid

43. Exercises on Surface Area Solve for the surface area of each given solid

44. Exercises on Surface Area Solve for the surface area of each given solid

45. Exercises on Surface Area Solve for the surface area of each given solid

46. Exercises on Surface Area Solve for the surface area of each given solid

47. Exercises on Surface Area Solve for the surface area of each given solid

48. Exercises on Surface Area Solve for the surface area of each given solid

49. Exercises on Surface Area Solve for the surface area of each given solid

50. Exercises on Surface Area Solve for the surface area of each given solid

51. Exercises on Surface Area Solve for the surface area of each given solid

52. Exercises on Surface Area Solve for the surface area of each given solid

53. Exercises on Surface Area Solve for the surface area of each given solid

54. Exercises on Surface Area Solve.

55. MORE Exercises on Surface Area Solve for the SA.

56. Exercises on Surface Area Solve.

57. Exercises on Surface Area Solve.

58. MORE Exercises on Surface Area Solve for the surface area of each solid (no answers given)

59. MORE Exercises on Surface Area Solve for the surface area of each solid (no answers given)

60. MORE Exercises on Surface Area Express the SA of each solid (no answers given)

61. MORE Exercises on Surface Area Solve for the SA of each solid (no answers given)

62. MORE Exercises on Surface Area Solve for the SA of each solid (no answers given)

63. MORE Exercises on Surface Area Solve for the surface area of each solid (no answers given)

64. MORE Exercises on Surface Area Solve for the SA of each solid (no answers given)