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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
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 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
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 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
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 288𝜋 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. 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
