3D Geometry: Chapter Questionscontent.njctl.org/courses/math/7th-grade/geometry/3d-geometry-7th... · 3D Geometry: Chapter Questions ... Which has a greater surface area: a square

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3D Geometry: Chapter Questions

1. What are the similarities and differences between prisms and pyramids?

2. How are polyhedrons named?

3. How do you find the cross-section of 3-Dimensional figures?

4. How do you find the volume of a prism or cylinder?

5. How are the volumes of prisms and pyramids related?

6. How do you find the Surface Area of a 3-Dimensional Figure?


3D Geometry: Chapter Problems

3 Dimensional Solids

Class Work

In 1-5, name the figure.

1. 2. 3. 4. 5.

In 6-10, give the number faces, edges, and vertices of each shape.

6. 7. 8.

9. triangular pyramid

10. square prism

Homework

In 11-15, name the figure.

11. 12. 13. 14. 15.

In 16-20, give the number faces, edges, and vertices of each shape.

16. 17. 18.

19. octagonal pyramid

20. rectangular prism


Cross Sections of 3-Dimensional Figures

Class Work

In 21-24, sketch the cross-section formed by cutting each figure horizontally.

21. 22. 23.

24.

In 25-28, sketch the cross-section formed by cutting each figure vertically.

25. Figure #1 Above 26. Figure #2 Above 27. Figure #3 Above 28. Figure #4 Above

Homework

In 29-33, sketch the cross-section formed by cutting each figure horizontally.

29. 30. 31.

32.

In 33-36, sketch the cross-section formed by cutting each figure vertically.

33. Figure #29 Above 34. Figure #30 Above 35. Figure #31 Above 36. Figure #32 Above


Volume of Prisms and Cylinders

Class Work

Find the volume of each figure.

37. 38. 39.

40. A 5 m x 3 m x 4 m rectangular prism

41. A cube with edge of 6 ft

42. A cylinder with height of 14 cm and base diameter of 10 cm

43. A triangular prism with a base area of 15 square inches and a height of 12 inches

44. A cylinder with base circumference of 8𝜋 and height 7.

45. A box has volume of 24 ft3 and a base of 2 ft by 3 ft, what is its height?

46. The community center is making a circular garden that will be 20 feet across. They want to fill it with 2 feet of potting soil. How much potting soil should be ordered?

47. A 2 foot wide path is being placed around the garden in question #10. If the path is 6 inches deep, how much stone needs to be ordered to make the path?

Homework

Find the volume of each figure.

48. 49. 50.

51. A 6m x 7m x 2m rectangular prism

52. A cube with edges of 8ft

53. A cylinder with height of 14cm and base diameter of 8cm

54. A pentagonal prism with a base area of 14 square inches and a height of 11 inches

55. A cylinder with base circumference of 6𝜋 and height 9.

56. A box has volume of 24 ft3 and a base of 2 ft by 4ft, what is its height?

57. The community center is making a circular garden that will be 18 feet across. They want to fill it with 1 foot of potting soil. How much potting soil should be ordered?


58. A 3 foot wide path is being placed around the garden in question #10. If the path is 8 inches deep, how much stone needs to be ordered to make the path?

Volume of Pyramids, Cones, and Spheres

Class Work

Find the volume of the figure.

59. 60. 61.

62. A pentagonal pyramid with base area of 12 cm2 and a height of 10 cm.

63. A cone with base circumference of 6𝜋 and height 9.

64. A square pyramid with a base perimeter of 12 ft and a height of 9 ft.

65. A sphere with a diameter of 8 m.

66. A cone with radius 4 ft and a height of 36 inches.

67. A small waffle cone is 4 inches across and 6 inches deep. Ice cream is filled even with the top. If it sells for $2, what is the cost per cubic inch?

68. A medium cone is 6 inches across and 8 inches deep. How much should it sell for if the cost per cubic inch is the same as the small cone in question #8?

Homework

Find the volume of the figure.

69. 70. 71.

72. A pentagonal pyramid with base area of 16 cm2 and a height of 12 cm.

73. A cone with base circumference of 8𝜋 and height 8.

74. A square pyramid with a base perimeter of 16 ft and a height of 12 ft.

75. A sphere with a diameter of 10 m.

76. A cone with radius 2 ft and a height of 24 inches.

77. A small waffle cone is 2 inches across and 6 inches deep. Ice cream is filled even with the top. If it sells for $2, what is the cost per cubic inch?


78. A medium cone is 4 inches across and 9 inches deep. How much should it sell for if the cost per cubic inch is the same as the small cone in question #8?

Surface Area of Prisms

Class Work

Find the surface area of the following figures.

79. 80. 81.

82. . 83. 84.

85. The photography club has a room that they are going to turn into a dark room. The room is 12 feet by 10 feet by 8 feet. The walls, ceiling and floor will receive 2 coats of a special paint that covers 40 square feet per gallon. How many gallons do they need to purchase?

86. A chef is making a cake that is best described as a square prism that is 1 ft by 1 ft by 9 inches and has 6 layers. How much area must the chef ice?

Homework

Find the surface area of the following figures.

87. 88. 89.

90. 91. 92.


93. The photography club has a room that they are going to turn into a dark room. The room is 14 feet by 11 feet by 10 feet. The walls, ceiling and floor will receive 2 coats of a special paint that covers 45 square feet per gallon. How many gallons do they need to purchase?

94. A chef is making a cake that is best described as a square prism that is 1 ft by 1 ft by 8 inches and has 8 layers. How much area must the chef ice?

Surface Area of Pyramids

Class Work

Find the surface area of the given figure.

95. 96. 97.

98. 99. 100.

101. Which has a greater surface area: a square pyramid with base edges of 8 mm and a slant height of

10 mm or a square pyramid with base edges of 10 mm and a slant height of 8 mm?

102. The Great Pyramid of Giza is a square pyramid with base edges of 480 ft and a slant height 512 ft. It was covered with lime stone to make it look like one solid highly polished monument. What is the area that was covered in the casing stones?


Homework


103. 104. 105.

106. 107. 108.

109. A square pyramid with base edges of 6 m and slant height of 10 m has its base edges doubled and its slant height tripled, how many times greater is the surface of the new pyramid?

110. The Louvre Pyramid is a square pyramid made of glass and steel in front of the Louvre Museum in Paris, France. It has base edges of 115 feet and a slant height of 91 feet. What is area that needed to be covered with glass?

Surface Area of a Cylinder

Class Work

Find the surface area of the figure given.

111. 112. 113.

114. 115. 116.


117. A cylinder with height 10 inches and base of 2 feet has what surface area?

118. Which is greater: A cylinder with radius 4 inches and height 6 inches or radius of 6 inches and

height of 4 inches, and by how much?

Homework

Find the surface area of the figure given.

119. 120. 121.

122. 123. 124.

125. A cylinder with height 20 inches and base of 1 foot has what surface area?

126. Which is greater: A cylinder with radius 10 inches and height 6 inches or radius of 6 inches and

height of 10 inches, and by how much?

Surface Area of Spheres

Class Work


127. 128. 129.

130. 131. 132.


133. Find the surface area of a sphere if its volume is 36𝜋 cm3.

134. The Earth has a diameter of about 8000 miles and 70% of the surface is covered by water. How

many square miles of land are there?

Homework


135. 136. 137.

138. 139. 140.

141. Find the surface area of a sphere if its volume is 288𝜋 cm3.

142. If the circumference of a soccer ball is 62.8 cm, what is its surface area?


UNIT REVIEW

Multiple Choice

1. How many edges are in a Rectangular Prism?

a. 6

b. 15

c. 12

d. 10

2. Name the figure:

a. Rectangular Pyramid

b. Triangular Prism

c. Rectangular Prism

d. Triangular Pyramid

3. Which of the following is a prism with squares for its side and faces?

a. b. c. d.

4. What is volume of a cylinder with a base of diameter 4m and a height of 6 m? (Use 3.14)

a. 75.36 m3

b. 301.44 m3

c. 908.32 m3

d. 1205.76 m3

5. A triangular pyramid has a base with area 12 ft2 and a height of 5 ft, what is the volume of the

pyramid?

a. 24 ft3

b. 30 ft3

c. 60 ft3

d. Cannot be determined

6. How many vertices are in an rectangular prism?

a. 6

b. 8

c. 10

d. 16

7. A square pyramid has base edges of 0.3 mm and a height of 10 cm, what is its volume?

a. 3.0 cm3

b. 9.0 mm3

c. 30 mm3

d. 900 mm3


13 ft

4 ft

8. A cube with edges 5 ft is compared to a cube with edges 10 ft. How many times bigger is the volume

of the larger cube?

a. 4

b. 6

c. 8

d. 875

9. A cube with edges 5 ft is compared to a cube with edges 10 ft. How many times bigger is the surface

area of the larger cube?

a. 4

b. 6

c. 8

d. 450

10. Which figure(s) has a square for its vertical cross section?

a. b. c. d.

11. What is volume of the given figure?

a. 100.48 ft2

b. 427.04 ft2

c. 326.56 ft2

d. 653.12 ft2

12. What is the surface area of a cylinder with a radius of 2 in and a height of 7 in?

a. 87.96 in2

b. 113.10 in2

c. 226.20 in2

d. 452.40 in2

13. What is the surface area?

a. 176 cm2

b. 203.67 cm2

c. 304.56 cm2

d. 310.24 cm2


Short Constructed Response – Write the correct answer for each question.

14. A rectangular storage tank is to have a height of 10 feet, a length of 5 feet and a width of 2 feet. It is

to be filled with water. What is weight of the water in a full tank if 1 ft3 of water weighs 62.4 lbs?

15. The volume of the cone, with a radius of 3 in, is 160 in3. Find its height.

16. Draw the horizontal and vertical cross-sections of the figure.

17. Find the volume of the figure shown, given the radius is 6 cm.

18. Glasses will be packed into a cardboard box that has dimensions of 12x10x6 inches. The factory will

put 30 boxes on each pallet. How much cardboard will be needed for each pallet of boxes?

http://upload.wikimedia.org/wikipedia/commons/7/7e/Sphere_wireframe_10deg_6r.svg


Extended Constructed Response - Solve the problem, showing all work. Partial credit may be given.

19. A cylindrical container of chicken broth has a radius of 2 inches and a height of 6 inches.

a. What is the volume of container?

b. A label is to be placed around the can of chicken broth. What is the area of the label? (Round to

the nearest hundredths)?

c. What is the surface area of the can?

d. If the can of chicken broth sells for $1.09 and the cost of the broth is $.20, the cost of the can is

$0.34, plus $0.002/in2 for the label, what is the profit for each can of broth sold?


Answer Key

1. Hexagonal Prism

2. Cylinder

3. Octagonal Prism

4. Cone

5. Pentagonal Pyramid

6. 10 faces, 16 vertices, 24 edges





11. Triangular Pyramid

12. Cylinder

13. Triangular Prism

14. Pentagonal Prism

15. Cone






21. Circle

22. Rectangle

23. Pentagon

24. Rectangle

25. Rectangle

26. Rectangle

27. Triangle

28. Rectangle if cut front to back, Triangle if cut

left to right

29. Rectangle

30. Triangle

31. Circle

32. Rectangle

33. Pentagon

34. Triangle

35. Triangle

36. Triangle

37. 96 ft3

38. 942 in3

39. 48 u3

40. 60 m3

41. 216 ft3

42. 1099 cm3

43. 180 in3

44. 351.68 u3

45. 4 feet

46. 628 ft3

47. 69.08 ft3

48. 240 u3

49. 180 ft3

50. 226.08 mm3

51. 84 m3

52. 512 ft3

53. 703.36 cm3

54. 154 in3

55. 254.34 u3

56. 3 feet

57. 254.34 ft3

58. 131.88 ft3

59. 40 u3

60. 75.36 ft3

61. 1436.03 cm3

62. 40 cm3

63. 84.78 u3

64. 27 ft3

65. 267.95 m3

66. 50.24 ft3

67. $0.08 per cubic inch

68. $6.03

69. 904.32 cm3

70. 96 u3

71. 414.48 ft3

72. 64 cm3

73. 133.97 u3

74. 64 ft3

75. 523.33 m3

76. 8.37 ft3

77. $0.32 per cubic inch

78. $12.06

79. 152 m²

80. 560 cm²

81. 1184 cm²

82. 488 in²

83. 3680 ft²

84. 500 cm²

85. 30 gallons

86. 1296 in²

87. 2640 ft²

88. 150 in²

89. 872 cm²

90. 360 cm²

91. 88 m²

92. 2706 cm²

93. 36 gallons


94. 1536 in²

95. 85 in²

96. 176 in²

97. 340 in²

98. 105.6 in²

99. 283 in²

100. 67.2 in²

101. Square pyramid with base edges of 10

mm and slant height of 8 mm is greater (260

mm²)

102. 721,920 ft²

103. 640 in²

104. 341 in²

105. 175 in²

106. 350.4 in²

107. 19.7 in²

108. 26.4 in²

109. 5.54 times greater (864 m² / 156 m²)

110. 34,155 ft²

111. 113.04 ft²

112. 533.8 in²

113. 1413 cm²

114. 1105.28 cm²

115. 150.72 m²

116. 1657.92 cm²

117. 1657.92 in²

118. Cylinder with radius of 6 in and height of

4 in is greater by 125.60 in²

119. 1413 cm²

120. 1004.8 m²

121. 678.24 cm²

122. 5878.08 mm²

123. 408.2 cm²

124. 1285.83 in²

125. 979.68 in²

126. Cylinder with radius of 10 in and height

of 6 in is greater by 401.92 in²

127. 706.5 km²

128. 803.84 ft²

129. 452.16 ft²

130. 12.56 ft²

131. 615.44 in²

132. 942 km²

133. 113.04 cm²

134. 60,288,000 square miles

135. 452.16 ft²

136. 452.16 in²

137. 200.96 ft²

138. 1133.54 km²

139. 113.04 mm²

140. 84.78 mm²

141. 452.16 cm²

142. 1256 cm²

UNIT REVIEW

1. B

2. B

3. A

4. A

5. C

6. B

7. B

8. C

9. A

10. A

11. D

12. B

13. B

14. 6240 LBS.

15. 5.66 IN

16. HORIZONTAL: 4 X 6

VERTICAL: 8 X 4

17. 904.78CM3

18. 15,120 IN2

19. A. 75.4 IN3

B. 75.4 IN2

C. 100.53 IN2

D. APPROXIMATELY 40 CENTS

3D Geometry: Chapter Questionscontent.njctl.org/courses/math/7th-grade/geometry/3d-geometry-7th... · 3D Geometry: Chapter Questions ... Which has a greater surface area: a square

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