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?
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3D Geometry: Chapter Problems
3 Dimensional Solids
Class Work
In 1-5, name the figure.
1.
2.
3.
4.
In 6-10, give the number faces, edges, and vertices of each shape.
6.
7.
5.
8.
9. triangular pyramid
10. square prism
Homework
In 11-15, name the figure.
11.
12.
13.
In 16-20, give the number faces, edges, and vertices of each shape.
16.
17.
14.
15.
18.
19. octagonal pyramid
20. rectangular prism
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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.
26.
27.
28.
Figure #1 Above
Figure #2 Above
Figure #3 Above
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.
34.
35.
36.
Figure #29 Above
Figure #30 Above
Figure #31 Above
Figure #32 Above
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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?
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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 cm 2 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?
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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.
84.
.
83.
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.
92.
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91.
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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.
100.
99.
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?
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Homework
Find the surface area of the given figure.
103.
104.
105.
106.
108.
107.
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.
116.
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115.
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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.
124.
123.
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.
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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?
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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
b. 9.0 mm3
c. 30 mm3
d. 900 mm3
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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.
11. What is volume of the given figure?
a. 100.48 ft2
b. 427.04 ft2
c. 326.56 ft2
d. 653.12 ft2
d.
4 ft
13 ft
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
b. 203.67 cm2
c. 304.56 cm2
d. 310.24 cm2
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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.
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?
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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?
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Answer Key
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
23.
24.
25.
26.
27.
28.
29.
30.
31.
32.
33.
34.
35.
36.
37.
38.
39.
40.
41.
42.
43.
44.
45.
46.
Hexagonal Prism
Cylinder
Octagonal Prism
Cone
Pentagonal Pyramid
10 faces, 16 vertices, 24 edges
6 faces, 6 vertices, 10 edges
8 faces, 12 vertices, 18 edges
4 faces, 4 vertices, 6 edges
6 faces, 8 vertices, 12 edges
Triangular Pyramid
Cylinder
Triangular Prism
Pentagonal Prism
Cone
4 faces, 4 vertices, 6 edges
5 faces, 6 vertices, 9 edges
7 faces, 10 vertices, 15 edges
9 faces, 9 vertices, 16 edges
6 faces, 8 vertices, 12 edges
Circle
Rectangle
Pentagon
Rectangle
Rectangle
Rectangle
Triangle
Rectangle if cut front to back, Triangle if cut
left to right
Rectangle
Triangle
Circle
Rectangle
Pentagon
Triangle
Triangle
Triangle
96 ft3
942 in3
48 u3
60 m3
216 ft3
1099 cm3
180 in3
351.68 u3
4 feet
628 ft3
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47.
48.
49.
50.
51.
52.
53.
54.
55.
56.
57.
58.
59.
60.
61.
62.
63.
64.
65.
66.
67.
68.
69.
70.
71.
72.
73.
74.
75.
76.
77.
78.
79.
80.
81.
82.
83.
84.
85.
86.
87.
88.
89.
90.
91.
92.
93.
69.08 ft3
240 u3
180 ft3
226.08 mm3
84 m3
512 ft3
703.36 cm3
154 in3
254.34 u3
3 feet
254.34 ft3
131.88 ft3
40 u3
75.36 ft3
1436.03 cm3
40 cm3
84.78 u3
27 ft3
267.95 m3
50.24 ft3
$0.08 per cubic inch
$6.03
904.32 cm3
96 u3
414.48 ft3
64 cm3
133.97 u3
64 ft3
523.33 m3
8.37 ft3
$0.32 per cubic inch
$12.06
152 m²
560 cm²
1184 cm²
488 in²
3680 ft²
500 cm²
30 gallons
1296 in²
2640 ft²
150 in²
872 cm²
360 cm²
88 m²
2706 cm²
36 gallons
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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
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138.
139.
140.
141.
142.
1133.54 km²
113.04 mm²
84.78 mm²
452.16 cm²
1256 cm²
UNIT REVIEW
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
B
B
A
A
C
B
B
C
A
A
D
B
B
6240 LBS.
5.66 IN
HORIZONTAL: 4 X 6
VERTICAL: 8 X 4
17. 904.78CM3
18. 15,120 IN2
19. A. 75.4 IN3
B. 75.4 IN2
C. 100.53 IN2
D. APPROXIMATELY 40 CENTS
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