1. Lesson 11.1 I can identify and name 3-dimensional figures
I can identify and name parts of 3-D figures (faces, bases, edges, vertices)
I can identify the shape of cross sections of 3-D figures and find the area of the cross sections
Lesson 11.1

2. solid
flat surfaces
polygons

3. 2
parallel
congruent 2
parallel
congruent 1
base
point
vertex
shape
base(s)

4. Rectangular prism
Pentagonal pyramid

5. Triangular prism
Trapezoidal prism

6. Square (or rectangular) pyramid
Pentagonal prism
Square (or rectangular) pyramid

7. ∆ABC ,
∆DEF
ABED,
BEFC,
ADFC AB BC CA DE EF FD BE CF AD
A, B, C, D, E, F

8. parallel bases
circles
circular
base
vertex

9. plane
rectangle
circle

10. rectangle
rectangle

11. 4 4 4
Isosceles triangle
square
A = ½ bh
A = bh
A = ½ 18(12)
A = 4(4)
A = 108 cm2
A = 16 un2

12. triangle
rectangle
A = ½ bh
A = bh
A = ½ 9(6)
A = 10(6)
A = 27 un2
A = 60 in2

13. ASSIGNMENT
11-1 worksheet

14. I can draw 2-d models for 3-d figures
I can surface area using nets
Lesson 11-2

15. 2
pattern
Top
Front
Left 1 6 2
Bottom
Right
Back

18. SA =
square + 4 triangles 10
= (40)
= 224 un2 8 8

19. 7 5 35 5 15 3 21 15
SA =
6 rectangles 5 35
= 142 un2 3 21 7

20. ≈ 477.52 cm2 SA = rectangle + 2 circles 15(8π) + 2π(42) 120π + 32π
= 152π 4 8π
≈ cm2 15

21. Investigation #1 - Prisms
Use the solids to answer the questions for each shape.
Draw pictures!
Shape of
Lateral Faces
Number of
Bases
Base
& Number of Sides
Number of Edges
Number of Vertices Ex
Octagonal Prism 8 2 24 16 1
Square
Prism 4 12
Rectangular Prism 3
Pentagonal 5 15 10
Triangular 9 6

22. Curved surface when flattened
Investigation #3 – Solids Involving Circles
Use the solids and the nets to answer the questions for each shape.
Draw pictures!
Number of
curved surfaces
Shape of
Curved surface when flattened
Bases
Base
Number of curved edges
Number of apexes
(like a vertex) 8
Cylinder 1 2
none 9
Cone 10
Sphere 11
Hemisphere

23. Investigation #2 - Pyramids
Use the solids to answer the questions for each shape.
Draw pictures!
Shape of
Lateral Faces
Number of
Bases
Base
& Number of Sides
Number of Edges
Number of Vertices Ex
Pentagonal Pyramid 5 1 10 6
Square
Pyramid 4 8
Octagonal 16 9 7
Triangular Pyramid 3

24. 11.1 Identify parts of 3d figures
Summarize the differences between prisms and pyramids
Prisms
Pyramids
Lateral Faces
Rectangles
Triangles
Bases
Two matching polygons
One polygon
Edges
Base edges times 3
Base edges times 2
Vertices
Base vertices times 2
Base vertices +1
Name
____________ prism
__________ pyramid
When the base is a circle it’s called a…
Cylinder
Cone
(name of base)
(name of base)

25. Warm Up
1. Draw and label a net for the following solid. Then find the surface area.

26. 3 6 2 3 2 3 8 16 8 24 16 8 8 24 8 3 2 3 2 2 6 2 3
SA = = 92 un2

27. ASSIGNMENT
11-2 worksheet

28. I can find the volume of prisms
I can find the volumes of cylinders
Lesson 11-3

29. V = Bh
B = area of base
V = πr2h

30. V = πr2h
= π(82)
(17.5)
= 1120π mm3
≈ mm3

31. V = πr2h
= π(82)
(30)
= 1920π cm3
≈ cm3

32. V = πr2h
= π(62)
(11.5)
= 414π in3
≈ in3

33. 24 ft
V = πr2h
= π(3.52)
(24)
= 294π ft3
≈ ft3

34. V = Bh
= 4.5
(6)
B = 1/2h(b1+b2)
= 27 cm3
= 1/2(1.5)(2 + 4)
= 4.5

35. V = Bh
= 93.6
(12)
B = 1/2Pa
= in3
= 1/2(36)(5.2)
= 93.6

36. V = Bh
= 150
(12)
B = bh
= 1800 ft3
= 10(15)
= 150

37. V = Bh
= 27
(10)
B = 1/2bh
= 270 un3
= 1/2(9)(6)
= 27

38. V = Bh
735 =
42h
17.5 cm = h

39. V = Bh
196 =
16B
16 = B
4 in by 4 in 16 ? ?

40. ASSIGNMENT
11-3 worksheet

41. I can find the volume of pyramids
I can find the volume of cones
Lesson 11-4

42. segment
vertex
base
height
lateral face
segment
vertex
perpendicular
base

43. V = 1/3 Bh
B = area of base
V = 1/3 πr2h

44. V = 1/3 πr2h
= 1/3 π(42)
(7)
= 37.3π in3
≈ in3

45. V = 1/3 πr2h 24
= 1/3 π(102)
(24)
= 800π ft3
≈ ft3

46. V = 1/3 πr2h 8
= 1/3 π(62)
(8)
= 96π cm3
≈ cm3

47. = 424.3π yd3 ≈ 1333.08 yd3 V = 1/3 πr2h = 1/3 π(102) (12.73) r = 10

48. V = 1/3 Bh
= 1/3 (64)
(10)
B = bh
= ft3
= 8(8)
= 64

49. 8
B = 1/2bh
V = 1/3 Bh
= 1/2(6)(8)
= 1/3 (24)
(15)
= 24
= 120 ft3

50. 4 3
V = 1/3 Bh
= 1/3 (48)
(3)
B = bh
= 48 yd3
= 8(6)
= 48

51. 5
V = 1/3 Bh 10 10
= 1/3 (100)
(12)
B = bh
= 400 cm3
= 10(10)
= 100

52. V = 1/3 πr2h 96π = 1/3 πr2 (8) π π 96 = 1/3 r2(8) 288 = r2(8) 36 = r2
π π
(3) (3)
96 = 1/3 r2(8)
288 = r2(8)
36 = r2
6 = r

53. V = 1/3 πr2h 2500π = 1/3 π 52 (h) π π 2500 = 1/3 (25)(h) 7500 = 25h
π π
(3) (3)
2500 = 1/3 (25)(h)
7500 = 25h
300 = h

54. ASSIGNMENT
11-4 worksheet

55. I can find surface area of spheres
I can find volume of spheres
Lesson 11-5

56. SA = 4πr2
V =
4πr3 3
V =
2πr3 3

57. V = = SA = 4πr2 = 4π(6)2 = 144π cm2 ≈ 452.39 cm2 4πr3 3 4π(6)3 3

58. V = SA = 4π(4)2 = 64π cm2 ≈ 201.06 cm2 4π(4)3 3 = 85.3π cm3

59. V =
2πr3 3 =
2π(16)3 3
= π m3
≈ m3

60. V =
2π(10)3 3
= 666.6π in3
≈ in 3

61. C = πd
SA = 4π(9.23)2
58 = πd
≈ m2
18.46 = d
9.23 = r

62. 9.23 = r
V =
4π(9.23)3 3
≈ cm3

63. V =
4πr3 3
288π =
4πr3 3
SA = 4π(6)2
= 144π cm2
216 = r3
6 = r

64. SA = 4πr2
324π = 4πr2
V =
4π(9)3 3
81 = r2
9 = r
= 972π in3

65. ASSIGNMENT
11-5 worksheet

66. I can find the volume of composite figures
Lesson 11-6

67. cone + cylinder cone: cylinder: Total : 57.9π ≈ 181.9 cm3 V = 1/3 πr2h4
cone:
cylinder:
V = 1/3 πr2h
V = πr2h
= 1/3 π(3)24
= π(3)25.1
= 12π
= 45.9π
Total : 57.9π
≈ cm3

68. triangular prism
V = Bh
= 120 (70)
= 8400
rectangular prism
V = Bh
Total = 29,400 ft3
= 2100 (10)
= 21000

69. ASSIGNMENT
11-6 worksheet

70. I can identify properties of similar solids
I can find volume and surface area of similar solids
Lesson 11-7

71. shape
size
a : b
a2 : b2
a3 : b3

72. congruent
similar
1 : 3

73. neither
similar
2 : 1

74. 1 : 2
8 : 5
12 : 22
or 1 : 4
82 : 52
or 64 : 25
13 : 23
or 1 : 8
83 : 53
or 512 :125

75. 12 : 15
4 : 5 4 5 10 x
12.5 m =
42 : 52
or 16 : 25 16 25
280 x
437.5 m2 =
43 : 53
or 64 :125 64
125
400 x m3 =

76. 8 : 6
4 : 3 4 3 11 x
8.25 cm = 16 9 x
325
42 : 32
or 16 : 9
cm2 =
43 : 33
or 64 :27 64 27
1345 x
cm3 =

77. ASSIGNMENT
11-6 worksheet