1. Please read the following and consider yourself in it.
An Affirmation
Please read the following and consider yourself in it.
I am capable of learning. I can accomplish mathematical tasks. I am ultimately responsible for my learning.

2. CCSS Content Standards
 MGSE9-12.G.GMD.1 Give informal arguments for geometric formulas.
a) Give informal arguments for the formulas of the circumference of a circle and area of a circle using dissection arguments and informal limit arguments.
b) Give informal arguments for the formula of the volume of a cylinder, pyramid, and cone using Cavalieri’s principle.
MGSE9-12.G.GMD.2 Give an informal argument using Cavalieri’s principle for the formulas for the volume of a sphere and other solid figures.
MGSE9-12.G.GMD.3 Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.
Visualize relationships between two-dimensional and three-dimensional objects
MGSE9-12.G.GMD.4 Identify the shapes of two-dimensional cross-sections of three-dimensional objects, and identify three-dimensional objects generated by rotations of two-dimensional objects.
CCSS

3. Objectives: For each objective write down the important words/phrases each one contains.
G.GMD.1-2 – SWBAT apply Cavalieri’s principle IOT formulate an informal proof for the volume of a cylinder, pyramid, cone, sphere and other solids.
G.GMD.4 – SWBAT identify the shapes of two-dimensional cross-sections of three-dimensional objects IOT evaluate the volume of the solid.
G.GMD.4 – SWBAT identify three-dimensional objects generated by rotations of two-dimensional objects IOT derive formulas for volumes of solids.
G.GMD.3 – SWBAT apply and calculate volumes of cylinders, pyramids, cones, and spheres IOT solve problems.
Then/Now

4. This is our Anchor Slide
Important Formulas!
This is our Anchor Slide
All our work will come back to these formulas!
Concept

5. lateral face lateral edge base edge altitude height lateral area axis
composite solid
Vocabulary

6. Concept

7. Find the lateral area of the regular hexagonal prism.
Lateral Area of a Prism
Find the lateral area of the regular hexagonal prism.
The bases are regular hexagons. So the perimeter of one base is 6(5) or 30 centimeters.
Lateral area of a prism
P = 30, h = 12
Multiply.
Answer:
Example 1

8. Find the lateral area of the regular hexagonal prism.
Lateral Area of a Prism
Find the lateral area of the regular hexagonal prism.
The bases are regular hexagons. So the perimeter of one base is 6(5) or 30 centimeters.
Lateral area of a prism
P = 30, h = 12
Multiply.
Answer: The lateral area is 360 square centimeters.
Example 1

9. Concept

10. Find the surface area of the rectangular prism.
Surface Area of a Prism
Find the surface area of the rectangular prism.
Example 2

11. Surface area of a prism L = Ph Substitution Simplify. Answer:
Example 2

12. Answer: The surface area is 360 square centimeters.
Surface Area of a Prism
Surface area of a prism
L = Ph
Substitution
Simplify.
Answer: The surface area is 360 square centimeters.
Example 2

13. Concept

14. L = 2rh Lateral area of a cylinder
Lateral Area and Surface Area of a Cylinder
Find the lateral area and the surface area of the cylinder. Round to the nearest tenth.
L = 2rh Lateral area of a cylinder
= 2(14)(18) Replace r with 14 and h with 18.
≈ Use a calculator.
Example 3

15. S = 2rh + 2r2 Surface area of a cylinder
Lateral Area and Surface Area of a Cylinder
S = 2rh + 2r2 Surface area of a cylinder
≈ (14)2 Replace 2rh with and r with 14.
≈ Use a calculator.
Answer:
Example 3

16. S = 2rh + 2r2 Surface area of a cylinder
Lateral Area and Surface Area of a Cylinder
S = 2rh + 2r2 Surface area of a cylinder
≈ (14)2 Replace 2rh with and r with 14.
≈ Use a calculator.
Answer: The lateral area is about square feet and the surface area is about square feet.
Example 3

17. L = 2rh Lateral area of a cylinder
Find Missing Dimensions
MANUFACTURING A soup can is covered with the label shown. What is the radius of the soup can?
L = 2rh Lateral area of a cylinder
125.6 = 2r(8) Replace L with 15.7 ● and h with 8.
125.6 = 16r Simplify.
2.5 ≈ r Divide each side by 16.
Example 4

18. Answer: The radius of the soup can is about 2.5 inches.
Find Missing Dimensions
Answer: The radius of the soup can is about 2.5 inches.
Example 4

19. Find the lateral area of the cylinder.
A ft2
B ft2
C ft2
D ft2
5-Minute Check 1

20. Find the lateral area of the cylinder.
A ft2
B ft2
C ft2
D ft2
5-Minute Check 1

21. Find the lateral area of the prism.
A. 150 in2
B. 126 in2
C. 108 in2
D. 96 in2
5-Minute Check 2

22. Find the lateral area of the prism.
A. 150 in2
B. 126 in2
C. 108 in2
D. 96 in2
5-Minute Check 2

23. Find the surface area of the prism.
A. 320 mm2
B. 400 mm2
C mm2
D. 502 mm2
5-Minute Check 3

24. Find the surface area of the prism.
A. 320 mm2
B. 400 mm2
C mm2
D. 502 mm2
5-Minute Check 3

25. Find the surface area of the cylinder.
A cm2
B cm2
C cm2
D cm2
5-Minute Check 4

26. Find the surface area of the cylinder.
A cm2
B cm2
C cm2
D cm2
5-Minute Check 4

27. The lateral area of a prism is 476 square meters
The lateral area of a prism is 476 square meters. The area of one of its bases is 25 square meters. What is the surface area of the prism?
A. 426 m2
B. 451 m2
C. 501 m2
D. 526 m2
5-Minute Check 5

28. The lateral area of a prism is 476 square meters
The lateral area of a prism is 476 square meters. The area of one of its bases is 25 square meters. What is the surface area of the prism?
A. 426 m2
B. 451 m2
C. 501 m2
D. 526 m2
5-Minute Check 5

29. regular pyramid slant height right cone oblique cone apothem
Vocabulary

30. Concept

31. Find the lateral area of the square pyramid.
Lateral Area of a Regular Pyramid
Find the lateral area of the square pyramid.
Lateral area of a regular pyramid
P = 2.5 ● 4 or 10, ℓ = 5
Answer:
Example 1

32. Find the lateral area of the square pyramid.
Lateral Area of a Regular Pyramid
Find the lateral area of the square pyramid.
Lateral area of a regular pyramid
P = 2.5 ● 4 or 10, ℓ = 5
Answer: The lateral area is 25 square centimeters.
Example 1

33. Concept

34. Find the surface area of the square pyramid to the nearest tenth.
Surface Area of a Square Pyramid
Find the surface area of the square pyramid to the nearest tenth.
Step 1 Find the slant height
c2 = a2 + b2 Pythagorean Theorem
ℓ2 = a = 6, b = 4, and c = ℓ
ℓ = Simplify.
Example 2

35. Step 2 Find the perimeter and area of the base.
Surface Area of a Square Pyramid
Step 2 Find the perimeter and area of the base.
P = 4 ● 8 or 32 m A = 82 or 64 m2
Step 3 Find the surface area of the pyramid.
S = Pℓ + B Surface area of a regular pyramid __ 1 2 __ 1 2
= (32) P = 32, ℓ = , B = 64
≈ Use a calculator.
Answer:
Example 2

36. Step 2 Find the perimeter and area of the base.
Surface Area of a Square Pyramid
Step 2 Find the perimeter and area of the base.
P = 4 ● 8 or 32 m A = 82 or 64 m2
Step 3 Find the surface area of the pyramid.
S = Pℓ + B Surface area of a regular pyramid __ 1 2 __ 1 2
= (32) P = 32, ℓ = , B = 64
≈ Use a calculator.
Answer: The surface area of the pyramid is about square meters.
Example 2

37. Find the surface area of the square pyramid to the nearest tenth.
A. 96 in2
B in2
C in2
D. 156 in2
Example 2

38. Find the surface area of the square pyramid to the nearest tenth.
A. 96 in2
B in2
C in2
D. 156 in2
Example 2

39. Step 1 Find the perimeter of the base. P = 6 ● 10.4 or 62.4 cm
Surface Area of a Regular Pyramid
Find the surface area of the regular pyramid. Round to the nearest tenth.
Step 1 Find the perimeter of the base.
P = 6 ● 10.4 or 62.4 cm
Example 3

40. Step 2 Find the length of the apothem and the area of the base.
Surface Area of a Regular Pyramid
Step 2 Find the length of the apothem and the area of the base.
A central angle of the hexagon is or 60°, so the angle formed in the triangle is 30°.
______
360° 6
Example 3

41. tan 30° = Write a trigonometric ratio to find the apothem a.
Surface Area of a Regular Pyramid
tan 30° = Write a trigonometric ratio to find the apothem a.
a = Solve for a.
a ≈ 9.0 Use a calculator.
A = Pa Area of a regular polygon
≈ (62.4)(9.0) Replace P with 62.4 and a width 9.0.
≈ Multiply.
So, the area of the base is approximately cm2.
Example 3

42. Step 3 Find the surface area of the pyramid.
Surface Area of a Regular Pyramid
Step 3 Find the surface area of the pyramid.
S = Pℓ + B Surface area of regular pyramid
≈ (62.4)(15) P = 62.4, ℓ = 15, and B ≈ 280.8
≈ Simplify.
Answer:
Example 3

43. Step 3 Find the surface area of the pyramid.
Surface Area of a Regular Pyramid
Step 3 Find the surface area of the pyramid.
S = Pℓ + B Surface area of regular pyramid
≈ (62.4)(15) P = 62.4, ℓ = 15, and B ≈ 280.8
≈ Simplify.
Answer: The surface area of the pyramid is about cm2.
Example 3

44. Find the surface area of the regular pyramid
Find the surface area of the regular pyramid. Round to the nearest tenth.
A. 198 in2
B in2
C in2
D in2
Example 3

45. Find the surface area of the regular pyramid
Find the surface area of the regular pyramid. Round to the nearest tenth.
A. 198 in2
B in2
C in2
D in2
Example 3

46. Concept

47. Lateral Area of a Cone
ICE CREAM A sugar cone has an altitude of 8 inches and a diameter of inches. Find the lateral area of the sugar cone.
If the cone has a diameter of then the radius Use the altitude and the radius to find the slant height with the Pythagorean Theorem.
Example 4

48. Step 1 Find the slant height ℓ.
Lateral Area of a Cone
Step 1 Find the slant height ℓ.
ℓ2 = Pythagorean Theorem
ℓ2 ≈ Simplify.
ℓ ≈ 8.1 Take the square root of each side.
Step 2 Find the lateral area L.
L = rℓ Lateral area of a cone
≈ (1.25)(8.1) r = 1.25 and ℓ ≈ 8.1
≈ 31.8
Answer:
Example 4

49. Step 1 Find the slant height ℓ.
Lateral Area of a Cone
Step 1 Find the slant height ℓ.
ℓ2 = Pythagorean Theorem
ℓ2 ≈ Simplify.
ℓ ≈ 8.1 Take the square root of each side.
Step 2 Find the lateral area L.
L = rℓ Lateral area of a cone
≈ (1.25)(8.1) r = 1.25 and ℓ ≈ 8.1
≈ 31.8
Answer: The lateral area of the sugar cone is about 31.8 square inches.
Example 4

50. HATS A conical birthday hat has an altitude of 6 inches and a diameter of 4 inches. Find the lateral area of the birthday hat.
A in.2
B in.2
C in.2
D in.2
Example 4

51. HATS A conical birthday hat has an altitude of 6 inches and a diameter of 4 inches. Find the lateral area of the birthday hat.
A in.2
B in.2
C in.2
D in.2
Example 4

52. Find the surface area of the cone. Round to the nearest tenth.
Surface Area of a Cone
Find the surface area of the cone. Round to the nearest tenth.
Estimate: S ≈ 3 ● 1.5 ● ● 2 or 19.5 cm2
S = rℓ + r2 Surface area of a cone
= (1.4)(3.2) + (1.4)2 r = 1.4 and ℓ = 3.2
≈ 20.2
Answer:
Example 5

53. Find the surface area of the cone. Round to the nearest tenth.
Surface Area of a Cone
Find the surface area of the cone. Round to the nearest tenth.
Estimate: S ≈ 3 ● 1.5 ● ● 2 or 19.5 cm2
S = rℓ + r2 Surface area of a cone
= (1.4)(3.2) + (1.4)2 r = 1.4 and ℓ = 3.2
≈ 20.2
Answer: The surface area of the cone is about square centimeters. This is close to the estimate, so the answer is reasonable.
Example 5

54. Concept

55. great circle
pole
hemisphere
Vocabulary

56. Concept

57. Find the surface area of the sphere. Round to the nearest tenth.
Surface Area of a Sphere
Find the surface area of the sphere. Round to the nearest tenth.
S = 4r2 Surface area of a sphere
= 4(4.5)2 Replace r with 4.5.
≈ Simplify.
Answer:
Example 1

58. Find the surface area of the sphere. Round to the nearest tenth.
Surface Area of a Sphere
Find the surface area of the sphere. Round to the nearest tenth.
S = 4r2 Surface area of a sphere
= 4(4.5)2 Replace r with 4.5.
≈ Simplify.
Answer: in2
Example 1

59. Find the surface area of the sphere. Round to the nearest tenth.
A in2
B in2
C in2
D in2
Example 1

60. Find the surface area of the sphere. Round to the nearest tenth.
A in2
B in2
C in2
D in2
Example 1

61. A. Find the surface area of the hemisphere.
Use Great Circles to Find Surface Area
A. Find the surface area of the hemisphere.
Find half the area of a sphere with the radius of 3.7 millimeters. Then add the area of the great circle.
Example 2A

62. Surface area of a hemisphere
Use Great Circles to Find Surface Area
Surface area of a hemisphere
Replace r with 3.7.
≈ 129.0
Use a calculator.
Answer:
Example 2A

63. Surface area of a hemisphere
Use Great Circles to Find Surface Area
Surface area of a hemisphere
Replace r with 3.7.
≈ 129.0
Use a calculator.
Answer: about mm2
Example 2A

64. Use Great Circles to Find Surface Area
B. Find the surface area of a sphere if the circumference of the great circle is 10 feet.
First, find the radius. The circumference of a great circle is 2r. So, 2r = 10 or r = 5.
Example 2B

65. S = 4r2 Surface area of a sphere = 4(5)2 Replace r with 5.
Use Great Circles to Find Surface Area
S = 4r2 Surface area of a sphere
= 4(5)2 Replace r with 5.
≈ Use a calculator.
Answer:
Example 2B

66. S = 4r2 Surface area of a sphere = 4(5)2 Replace r with 5.
Use Great Circles to Find Surface Area
S = 4r2 Surface area of a sphere
= 4(5)2 Replace r with 5.
≈ Use a calculator.
Answer: about ft2
Example 2B

67. Use Great Circles to Find Surface Area
C. Find the surface area of a sphere if the area of the great circle is approximately 220 square meters.
First, find the radius. The area of a great circle is r2. So, r2 = 220 or r ≈ 8.4.
Example 2C

68. S = 4r2 Surface area of a sphere ≈ 4(8.4)2 Replace r with 5.
Use Great Circles to Find Surface Area
S = 4r2 Surface area of a sphere
≈ 4(8.4)2 Replace r with 5.
≈ Use a calculator.
Answer:
Example 2C

69. S = 4r2 Surface area of a sphere ≈ 4(8.4)2 Replace r with 5.
Use Great Circles to Find Surface Area
S = 4r2 Surface area of a sphere
≈ 4(8.4)2 Replace r with 5.
≈ Use a calculator.
Answer: about m2
Example 2C

70. A. Find the surface area of the hemisphere.
A m2
B m2
C m2
D m2
Example 2A

71. A. Find the surface area of the hemisphere.
A m2
B m2
C m2
D m2
Example 2A

72. B. Find the surface area of a sphere if the circumference of the great circle is 8 feet.
A ft2
B ft2
C ft2
D ft2
Example 2B

73. B. Find the surface area of a sphere if the circumference of the great circle is 8 feet.
A ft2
B ft2
C ft2
D ft2
Example 2B

74. C. Find the surface area of the sphere if the area of the great circle is approximately 160 square meters.
A. 320 ft2
B. 440 ft2
C. 640 ft2
D. 720 ft2
Example 2C

75. C. Find the surface area of the sphere if the area of the great circle is approximately 160 square meters.
A. 320 ft2
B. 440 ft2
C. 640 ft2
D. 720 ft2
Example 2C

76. Concept

77. Volumes of Spheres and Hemispheres
A. Find the volume a sphere with a great circle circumference of 30 centimeters. Round to the nearest tenth.
Find the radius of the sphere. The circumference of a great circle is 2r. So, 2r = 30 or r = 15.
Volume of a sphere
(15)3 r = 15
≈ 14,137.2 cm3 Use a calculator.
Example 3A

78. 1. Please re-examine the Objectives which ones have been addressed today and what key words/activities helped you make your decision?
2. From the Textbook Pages

79. Please read the following and consider yourself in it.
An Affirmation
Please read the following and consider yourself in it.
I am capable of learning. I can accomplish mathematical tasks. I am ultimately responsible for my learning.

80.  MGSE9-12.G.GMD.1 Give informal arguments for geometric formulas.
Content Standards
 MGSE9-12.G.GMD.1 Give informal arguments for geometric formulas.
a) Give informal arguments for the formulas of the circumference of a circle and area of a circle using dissection arguments and informal limit arguments.
b) Give informal arguments for the formula of the volume of a cylinder, pyramid, and cone using Cavalieri’s principle.
MGSE9-12.G.GMD.2 Give an informal argument using Cavalieri’s principle for the formulas for the volume of a sphere and other solid figures.
MGSE9-12.G.GMD.3 Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.
Visualize relationships between two-dimensional and three-dimensional objects
MGSE9-12.G.GMD.4 Identify the shapes of two-dimensional cross-sections of three-dimensional objects, and identify three-dimensional objects generated by rotations of two-dimensional objects.
CCSS

81. Objectives: For each objective write down the important words/phrases each one contains.
G.GMD.1-2 – SWBAT apply Cavalieri’s principle IOT formulate an informal proof for the volume of a cylinder, pyramid, cone, sphere and other solids.
G.GMD.4 – SWBAT identify the shapes of two-dimensional cross-sections of three-dimensional objects IOT evaluate the volume of the solid.
G.GMD.4 – SWBAT identify three-dimensional objects generated by rotations of two-dimensional objects IOT derive formulas for volumes of solids.
G.GMD.3 – SWBAT apply and calculate volumes of cylinders, pyramids, cones, and spheres IOT solve problems.
Then/Now

82. Concept

83. Find the volume of the prism.
Volume of a Prism
Find the volume of the prism.
V Bh Volume of a prism
1500 Simplify.
Answer:
Example 1

84. Find the volume of the prism.
Volume of a Prism
Find the volume of the prism.
V Bh Volume of a prism
1500 Simplify.
Answer: The volume of the prism is 1500 cubic centimeters.
Example 1

85. Find the volume of the prism.
A in3
B in3
C in3
D in3
Example 1

86. Find the volume of the prism.
A in3
B in3
C in3
D in3
Example 1

87. Concept

88. Find the volume of the cylinder to the nearest tenth.
Volume of a Cylinder
Find the volume of the cylinder to the nearest tenth.
Volume of a cylinder
= (1.8)2(1.8) r = 1.8 and h = 1.8
≈ 18.3 Use a calculator.
Answer:
Example 2

89. Find the volume of the cylinder to the nearest tenth.
Volume of a Cylinder
Find the volume of the cylinder to the nearest tenth.
Volume of a cylinder
= (1.8)2(1.8) r = 1.8 and h = 1.8
≈ 18.3 Use a calculator.
Answer: The volume is approximately 18.3 cm3.
Example 2

90. Concept

91. Find the volume of the oblique cylinder to the nearest tenth.
Volume of an Oblique Solid
Find the volume of the oblique cylinder to the nearest tenth.
To find the volume, use the formula for a right cylinder.
Volume of a cylinder
r 15, h 25
Use a calculator.
Answer:
Example 3

92. Find the volume of the oblique cylinder to the nearest tenth.
Volume of an Oblique Solid
Find the volume of the oblique cylinder to the nearest tenth.
To find the volume, use the formula for a right cylinder.
Volume of a cylinder
r 15, h 25
Use a calculator.
Answer: The volume is approximately 17,671.5 cubic feet.
Example 3

93. Find the volume of the oblique cylinder to the nearest tenth.
A cm3
B. 16,725.8 cm3
C cm3
D cm3
Example 3

94. Find the volume of the oblique cylinder to the nearest tenth.
A cm3
B. 16,725.8 cm3
C cm3
D cm3
Example 3

95. Comparing Volumes of Solids
Prisms A and B have the same width and height, but different lengths. If the volume of Prism B is 128 cubic inches greater than the volume of Prism A, what is the length of each prism?
Prism A
Prism B
A 12 B 8
C 4 D 3.5
Example 4

96. Volume of Prism A = 128 Write an equation.
Comparing Volumes of Solids
Read the Test Item
You know the volume of each solid and that the difference between their volumes is 128 cubic inches.
Solve the Test Item
Volume of Prism B –
Volume of Prism A = 128 Write an equation.
4x ● 9 – 4x ● 5 = 128 Use V = Bh.
16x = 128 Simplify.
x = 8 Divide each side by 16.
Answer:
Example 4

97. Volume of Prism A = 128 Write an equation.
Comparing Volumes of Solids
Read the Test Item
You know the volume of each solid and that the difference between their volumes is 128 cubic inches.
Solve the Test Item
Volume of Prism B –
Volume of Prism A = 128 Write an equation.
4x ● 9 – 4x ● 5 = 128 Use V = Bh.
16x = 128 Simplify.
x = 8 Divide each side by 16.
Answer: The length of each prism is 8 inches. The correct answer is B.
Example 4

98. Concept

99. Find the volume of the square pyramid.
Volume of a Pyramid
Find the volume of the square pyramid.
Volume of a pyramid
s 3, h 7 21
Multiply.
Answer:
Example 1

100. Find the volume of the square pyramid.
Volume of a Pyramid
Find the volume of the square pyramid.
Volume of a pyramid
s 3, h 7 21
Multiply.
Answer: The volume of the pyramid is 21 cubic inches.
Example 1

101. Brad is building a model pyramid for a social studies project
Brad is building a model pyramid for a social studies project. The model is a square pyramid with a base edge of 8 feet and a height of 6.5 feet. Find the volume of the pyramid.
A. 416 ft3 B. C. D.
Example 1

102. Brad is building a model pyramid for a social studies project
Brad is building a model pyramid for a social studies project. The model is a square pyramid with a base edge of 8 feet and a height of 6.5 feet. Find the volume of the pyramid.
A. 416 ft3 B. C. D.
Example 1

103. Concept

104. A. Find the volume of the oblique cone to the nearest tenth.
Volume of a Cone
A. Find the volume of the oblique cone to the nearest tenth.
Example 2A

105. Volume of a cone r = 9.1, h = 25 ≈ 2168.0 Use a calculator. Answer:
Example 2A

106. Answer: The volume of the cone is approximately 2168.0 cubic feet.
Volume of a Cone
Volume of a cone
r = 9.1, h = 25 ≈
Use a calculator.
Answer: The volume of the cone is approximately cubic feet.
Example 2A

107. B. Find the volume of the cone to the nearest tenth.
Volume of a Cone
B. Find the volume of the cone to the nearest tenth.
Example 2B

108. Volume of a cone r = 5, h = 12 ≈ 314.2 Use a calculator. Answer:
Example 2B

109. Answer: The volume of the cone is approximately 314.2 cubic inches.
Volume of a Cone
Volume of a cone
r = 5, h = 12
≈ 314.2
Use a calculator.
Answer: The volume of the cone is approximately cubic inches.
Example 2B

110. A. Find the volume of the oblique cone to the nearest tenth.
A m3
B. 27,463.2 m3
C m3
D m3
Example 2A

111. A. Find the volume of the oblique cone to the nearest tenth.
A m3
B. 27,463.2 m3
C m3
D m3
Example 2A

112. B. Find the volume of the cone to the nearest tenth.
A m3
B m3
C m3
D m3
Example 2B

113. B. Find the volume of the cone to the nearest tenth.
A m3
B m3
C m3
D m3
Example 2B

114. Find Real-World Volumes
SCULPTURE At the top of a stone tower is a pyramidion in the shape of a square pyramid. This pyramid has a height of 52.5 centimeters and the base edges are 36 centimeters. What is the volume of the pyramidion? Round to the nearest tenth.
Volume of a pyramid
B = 36 ● 36, h = 52.5
Simplify.
Answer:
Example 3

115. Answer: The volume of the pyramidion is 22,680 cubic centimeters.
Find Real-World Volumes
SCULPTURE At the top of a stone tower is a pyramidion in the shape of a square pyramid. This pyramid has a height of 52.5 centimeters and the base edges are 36 centimeters. What is the volume of the pyramidion? Round to the nearest tenth.
Volume of a pyramid
B = 36 ● 36, h = 52.5
Simplify.
Answer: The volume of the pyramidion is 22,680 cubic centimeters.
Example 3

116. SCULPTURE In a botanical garden is a silver pyramidion in the shape of a square pyramid. This pyramid has a height of 65 centimeters and the base edges are 30 centimeters. What is the volume of the pyramidion? Round to the nearest tenth.
A. 18,775 cm3
B. 19,500 cm3
C. 20,050 cm3
D. 21,000 cm3
Example 3

117. SCULPTURE In a botanical garden is a silver pyramidion in the shape of a square pyramid. This pyramid has a height of 65 centimeters and the base edges are 30 centimeters. What is the volume of the pyramidion? Round to the nearest tenth.
A. 18,775 cm3
B. 19,500 cm3
C. 20,050 cm3
D. 21,000 cm3
Example 3

118. Concept

119. 1. Please re-examine the Objectives which ones have been addressed today and what key words/activities helped you make your decision?
2. From the Textbook Pages