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3D Geometry: Chapter Questions 1. What Are the Similarities And 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 Nets Class Work In 21-25, identify the 3-dimensional figure from its net. 21. 22. 23. 24. In 25-28, draw the net for the stated figure. 25. Rectangular Pyramid 26. A soda can 27. A die 28. A piece of pizza Homework In 29-32, identify the 3-dimensional figure from its net. 29. 30. 31. 32. In 33-36, draw the net for the stated figure. 33. Hexagonal Prism 34. A car tire 35. A 4x4 fence post 36. A piece of apple pie 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 8휋 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 6휋 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 6휋 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 8휋 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 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 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 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 36휋 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. 138. 139. 140. 141. Find the surface area of a sphere if its volume is 288휋 cm3. 142. If the circumference of a soccer ball is 62.8 cm, what is its surface area? Answer Key 1. Hexagonal Prism 2. Cylinder 3. Octagonal Prism 4. Cone 5. Pentagonal Pyramid 6. 10 faces, 16 vertices, 24 edges 7. 6 faces, 6 vertices, 10 edges 8. 8 faces, 12 vertices, 18 edges 9. 4 faces, 4 vertices, 6 edges 10. 6 faces, 8 vertices, 12 edges 11. Triangular Pyramid 12. Cylinder 13. Triangular Prism 14. Pentagonal Prism 15. Cone 16. 4 faces, 4 vertices, 6 edges 17. 5 faces, 6 vertices, 9 edges 18. 7 faces, 10 vertices, 15 edges 19. 9 faces, 9 vertices, 16 edges 20. 6 faces, 8 vertices, 12 edges 21. Pentagonal Pyramid 22.
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