# 3D Geometry: Chapter Questions 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.

1. Figure #1 Above
2. Figure #2 Above
3. Figure #3 Above
4. 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.

1. Figure #29 Above
2. Figure #30 Above
3. Figure #31 Above
4. Figure #32 Above

Volume of Prisms and Cylinders

Class Work

Find the volume of each figure.

37.38.39.

1. A 5m x 3m x 4m rectangular prism
1. A cube with edge of 6ft
1. A cylinder with height of 14cm and base diameter of 10cm
1. A triangular prism with a base area of 15 square inches and a height of 12 inches
1. A cylinder with base circumference of 8 and height 7.
1. A box has volume of 24 ft3 and a base of 2 ft by 3ft, what is its height?
1. 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?
1. 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.

1. A 6m x 7m x 2m rectangular prism
1. A cube with edges of 8ft
1. A cylinder with height of 14cm and base diameter of 8cm
1. A pentagonal prism with a base area of 14 square inches and a height of 11 inches
1. A cylinder with base circumference of 6 and height 9.
1. A box has volume of 24 ft3 and a base of 2 ft by 4ft, what is its height?
1. 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?
2. 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.

1. A pentagonal pyramid with base area of 12 cm2 and a height of 10cm.
1. A cone with base circumference of 6 and height 9.
1. A square pyramid with a base perimeter of 12 ft and a height of 9 ft.
1. A sphere with a diameter of 8m.
1. A cone with radius 4 ft and a height of 36 inches.
1. 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?
1. 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.

1. A pentagonal pyramid with base area of 16 cm2 and a height of 12cm.
1. A cone with base circumference of 8 and height 8.
1. A square pyramid with a base perimeter of 16 ft and a height of 12 ft.
1. A sphere with a diameter of 10m.
1. A cone with radius 2 ft and a height of 24 inches.
1. 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?
2. 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.

1. 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?
1. A chef is making a cake that is best described as a square prism that is 1 ft by 1ft 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.

1. 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?
1. A chef is making a cake that is best described as a square prism that is 1 ft by 1ft 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.

1. 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?
1. 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.

1. A square pyramid with base edges of 6m and slant height of 10m has its base edges doubled and its slant height tripled, how many times greater is the surface of the new pyramid?
1. 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 20inches 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 36cm3.

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 288cm3.

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?
2. 6
3. 15
4. 12
5. 10
1. Name the figure:
2. Rectangular Pyramid
3. Triangular Prism
4. Rectangular Prism
5. Triangular Pyramid
1. Which of the following is a prism with squares for its side and faces?

a.b.c.d.

1. 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.1205.76m3

1. A triangular pyramid has a base with area 12 ft2 and a height of 5 ft, what is the volume of the pyramid?
2. 24 ft3
3. 30 ft3
4. 60 ft3
5. Cannot be determined
1. How many vertices are in an rectangular prism?
2. 6
3. 8
4. 10
5. 16
1. A square pyramid has base edges of 0.3 mm and a height of 10 cm, what is its volume?
2. 3.0 cm3
3. 9.0 mm3
4. 30 mm3
5. 900 mm3
1. 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?
2. 4
3. 6
4. 8
5. 875
1. 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?
2. 4
3. 6
4. 8
5. 450
1. Which figure(s) has a square for its vertical cross section?

a.b.c.d.

1. What is volume of the given figure?
2. 100.48 ft2
3. 427.04 ft2
4. 326.56 ft2
5. 653.12 ft2
1. What is the surface area of a cylinder with a radius of 2 in and a height of 7 in?
2. 87.96 in2
3. 113.10 in2
4. 226.20 in2
5. 452.40 in2
1. What is the surface area?
2. 176 cm2
3. 203.67 cm2
4. 304.56 cm2
5. 310.24 cm2

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

1. 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 62.4lbs?
1. The volume of the cone, with a radius of 3 in, is 160 in3. Find its height.
1. Draw the horizontal and vertical cross-sections of the figure.
1. Find the volume of the figure shown, given the radius is 6 cm.
1. 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.

1. A cylindrical container of chicken broth has a radius of 2 inches and a height of 6 inches.
1. What is the volume of container?
1. A label is to be placed around the can of chicken broth. What is the area of the label? (Round to the nearest hundredths)?
1. What is the surface area of the can?
1. 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

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. 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

1. 904.78CM3
2. 15,120 IN2
3. A. 75.4 IN3

B. 75.4 IN2

C. 100.53 IN2

D. APPROXIMATELY 40 CENTS

NJ Center for Teaching and Learning