3D Geometry: Chapter Questions

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

2. How are named?

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

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

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. 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. 34. A car tire 35. A 4x4 fence post 36. A piece of apple pie

Volume of Prisms and 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 with of 6 ft

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

43. A 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 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. 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. Decagonal Prism 23. Cylinder 24. Heptagonal Pyramid 25. Various ways to draw. One example: Rectangular Pyramid

26. Various ways to draw. One example: Cylinder

27. Various ways to draw. One example: Cube

28. Various ways to draw. One example: Triangular Prism

29. Square Pyramid 30. Pentagonal Pyramid 31. Pentagonal Prism 32. Triangular Prism 33. Various ways to draw. One example: Hexagonal Prism

34. Various ways to draw. One example: Cylinder

35. Various ways to draw. One example: Square Prism

36. Various ways to draw. One example: Triangular Prism

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. 1055.04 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. 846.23 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. 628 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. 56.52 mm² 141. 452.16 cm² 142. 1256 cm²