3D Geometry: Chapter Questions
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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?
NJ Center for Teaching and Learning www.njctl.org 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
NJ Center for Teaching and Learning www.njctl.org 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
NJ Center for Teaching and Learning www.njctl.org 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 8 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 6 and height 9.
NJ Center for Teaching and Learning www.njctl.org 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 6 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 8 and height 8.
NJ Center for Teaching and Learning www.njctl.org 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.
NJ Center for Teaching and Learning www.njctl.org 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?
NJ Center for Teaching and Learning www.njctl.org Homework Find the surface area of the given figure. 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
NJ Center for Teaching and Learning www.njctl.org 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.
NJ Center for Teaching and Learning www.njctl.org 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 Find the surface area of the given figure.
127. 128. 129.
130. 131. 132.
133. Find the surface area of a sphere if its volume is 36 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 Find the surface area of the given figure.
135. 136. 137.
NJ Center for Teaching and Learning www.njctl.org 138. 139. 140.
141. Find the surface area of a sphere if its volume is 288 cm3.
142. If the circumference of a soccer ball is 62.8 cm, what is its surface area?
NJ Center for Teaching and Learning www.njctl.org 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
NJ Center for Teaching and Learning www.njctl.org b. 9.0 mm3 c. 30 mm3 d. 900 mm3
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
NJ Center for Teaching and Learning www.njctl.org 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.
NJ Center for Teaching and Learning www.njctl.org 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?
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?
NJ Center for Teaching and Learning www.njctl.org Answer Key
1. Hexagonal Prism 25. Rectangle
2. Cylinder 26. Rectangle
3. Octagonal Prism 27. Triangle
4. Cone 28. Rectangle if cut front to back, Triangle if cut left to right 5. Pentagonal Pyramid 29. Rectangle 6. 10 faces, 16 vertices, 24 edges 30. Triangle 7. 6 faces, 6 vertices, 10 edges 31. Circle 8. 8 faces, 12 vertices, 18 edges 32. Rectangle 9. 4 faces, 4 vertices, 6 edges 33. Pentagon 10. 6 faces, 8 vertices, 12 edges 34. Triangle 11. Triangular Pyramid 35. Triangle 12. Cylinder 36. Triangle 13. Triangular Prism 37. 96 ft3 14. Pentagonal Prism 38. 942 in3 15. Cone 39. 48 u3 16. 4 faces, 4 vertices, 6 edges 40. 60 m3 17. 5 faces, 6 vertices, 9 edges 41. 216 ft3 18. 7 faces, 10 vertices, 15 edges 42. 1099 cm3 19. 9 faces, 9 vertices, 16 edges 43. 180 in3 20. 6 faces, 8 vertices, 12 edges 44. 351.68 u3 21. Circle 45. 4 feet 22. Rectangle 46. 628 ft3 23. Pentagon 47. 69.08 ft3 24. Rectangle 48. 240 u3
NJ Center for Teaching and Learning www.njctl.org 49. 180 ft3 74. 64 ft3
50. 226.08 mm3 75. 523.33 m3
51. 84 m3 76. 8.37 ft3
52. 512 ft3 77. $0.32 per cubic inch
53. 703.36 cm3 78. $12.06
54. 154 in3 79. 152 m²
55. 254.34 u3 80. 560 cm²
56. 3 feet 81. 1184 cm²
57. 254.34 ft3 82. 488 in²
58. 131.88 ft3 83. 3680 ft²
59. 40 u3 84. 500 cm²
60. 75.36 ft3 85. 30 gallons
61. 1436.03 cm3 86. 1296 in²
62. 40 cm3 87. 2640 ft²
63. 84.78 u3 88. 150 in²
64. 27 ft3 89. 872 cm²
65. 267.95 m3 90. 360 cm²
66. 50.24 ft3 91. 88 m²
67. $0.08 per cubic inch 92. 2706 cm²
68. $6.03 93. 36 gallons
69. 904.32 cm3 94. 1536 in²
70. 96 u3 95. 85 in²
71. 414.48 ft3 96. 176 in²
72. 64 cm3 97. 340 in²
73. 133.97 u3 98. 105.6 in²
NJ Center for Teaching and Learning www.njctl.org 99. 283 in² 123. 408.2 cm²
100. 67.2 in² 124. 1285.83 in²
101. Square pyramid with base edges of 10 125. 979.68 in² mm and slant height of 8 mm is greater (260 mm²) 126. Cylinder with radius of 10 in and height of 6 in is greater by 401.92 in² 102. 721,920 ft² 127. 706.5 km² 103. 640 in² 128. 803.84 ft² 104. 341 in² 129. 452.16 ft² 105. 175 in² 130. 12.56 ft² 106. 350.4 in² 131. 615.44 in² 107. 19.7 in² 132. 942 km² 108. 26.4 in² 133. 113.04 cm² 109. 5.54 times greater (864 m² / 156 m²) 134. 60,288,000 square miles 110. 34,155 ft² 135. 452.16 ft² 111. 113.04 ft² 136. 452.16 in² 112. 533.8 in² 137. 200.96 ft² 113. 1413 cm² 138. 1133.54 km² 114. 1105.28 cm² 139. 113.04 mm² 115. 150.72 m² 140. 84.78 mm² 116. 1657.92 cm² 141. 452.16 cm² 117. 1657.92 in² 142. 1256 cm² 118. Cylinder with radius of 6 in and height of 4 in is greater by 125.60 in² UNIT REVIEW 119. 1413 cm² 1. B 120. 1004.8 m² 2. B 3. A 121. 678.24 cm² 4. A 122. 5878.08 mm² 5. C
NJ Center for Teaching and Learning www.njctl.org 6. B 7. B VERTICAL: 8 X 4 8. C
9. A 10. A 11. D 12. B 13. B 14. 6240 LBS. 15. 5.66 IN 17. 904.78CM3 16. HORIZONTAL: 4 X 6 18. 15,120 IN2 19. A. 75.4 IN3 B. 75.4 IN2 C. 100.53 IN2 D. APPROXIMATELY 40 CENTS
NJ Center for Teaching and Learning www.njctl.org