3 Dimensional Geometry Chapter Questions
1. What are the differences between prisms and pyramids? Cylinders and cones?
2. What is volume and how is it found?
3. How are the volumes of cylinders, cones and spheres related?
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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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Volume of Prisms and Cylinders
Class Work
Find the volume of each figure.
21.
22.
23.
24. A 5 m x 3 m x 4 m rectangular prism
25. A cube with edge of 6 ft
26. A cylinder with height of 14 cm and base diameter of 10 cm. Use the 𝜋 button on your calculator.
27. A triangular prism with a base area of 15 square inches and a height of 12 inches
28. A cylinder with base circumference of 8𝜋 and height 7. Use 3.14 as your value of 𝜋.
29. A cylinder with a height of 5 in and a radius of 6 in. Leave your answer in terms of 𝜋.
30. A box has volume of 24 ft3 and a base of 2 ft by 3 ft, what is its height?
31. 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?
32. A 2 foot wide path is being placed around the garden in question #30. If the path is 6 inches deep,
how much stone needs to be ordered to make the path?
33. A circular pool has a diameter of 40 feet and a height of 4.5 feet. Find the amount of water needed to
fill the pool if the water line is 4 feet above the ground. Leave your answer in terms of 𝜋.
Homework
Find the volume of each figure.
34.
35.
36.
37. A 6 m x 7 m x 2 m rectangular prism
38. A cube with edges of 8 ft
39. A cylinder with height of 14 cm and base diameter of 8 cm. Use the 𝜋 button on your calculator.
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40. A pentagonal prism with a base area of 14 square inches and a height of 11 inches
41. A cylinder with base circumference of 6𝜋 and height 9. Use the 𝜋 button on your calculator.
42. A cylinder with a radius of 6 and height 12. Leave your answer in terms of 𝜋.
43. A box has volume of 24 ft3 and a base of 2 ft by 4 ft, what is its height?
44. 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?
45. A 3 foot wide path is being placed around the garden in question #44. If the path is 8 inches deep,
how much stone needs to be ordered to make the path?
46. A circular pool has a diameter of 50 feet and a height of 3.5 feet. Find the amount of water needed to
fill the pool if the water line is 3 feet above the ground. Leave your answer in terms of 𝜋.
Volume of Pyramids, Cones, and Spheres
Class Work
Find the volume of the figure.
47.
48.
49.
50. A pentagonal pyramid with base area of 12 cm 2 and a height of 10 cm.
51. A cone with base circumference of 6𝜋 and height 9. Use the 𝜋 button on your calculator.
52. A square pyramid with a base perimeter of 12 ft and a height of 9 ft.
53. A sphere with a diameter of 8 m. Use the 𝜋 button on your calculator.
54. A cone with a diameter of 12 cm and a height of 8 cm. Leave your answer in terms of 𝜋.
55. A cone with radius 4 ft and a height of 36 inches. Use 3.14 as your value of 𝜋.
56. Find out how much air is needed to inflate a basketball that has a radius of 4.75 inches. Leave your
answer in terms of 𝜋.
57. 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?
58. 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 #57?
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59. The figure shows a right circular cylinder & a right circular cone. The cylinder and cone have the
same base and the same height.
5 ft
5 ft
3 ft
3 ft
a) What is the volume of the cylinder, in cubic feet? Leave your answer in terms of 𝜋.
b) What is the ratio of the cone’s volume to the cylinder’s volume?
Homework
Find the volume of the figure.
60.
61.
62.
63. A pentagonal pyramid with base area of 16 cm2 and a height of 12 cm.
64. A cone with base circumference of 8𝜋 and height 8. Use the 𝜋 button on your calculator.
65. A square pyramid with a base perimeter of 16 ft and a height of 12 ft.
66. A sphere with a radius of 4 cm. Leave your answer in terms of 𝜋.
67. A sphere with a diameter of 10 m. Use the 𝜋 button on your calculator.
68. A cone with radius 2 ft and a height of 24 inches. Use 3.14 as your value of 𝜋.
69. Find out how much air is needed to inflate a basketball that has a diameter of 9.12 inches. Leave
your answer in terms of 𝜋.
70. 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?
71. 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 #70?
72. The figure shows a right circular cylinder & a right circular cone. The cylinder and cone have the
same base and the same height.
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6 ft
6 ft
2 ft
2 ft
a) What is the volume of the cone, in cubic feet? Leave your answer in terms of 𝜋.
b) What is the ratio of the cone’s volume to the cylinder’s volume?
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Unit Review
3D Geometry Multiple Choice Questions
1. Name the figure that is made of 2 congruent, circular bases, which are parallel to one
another, and all sides are curved.
a. cone
b. cylinder
c. pyramid
d. rectangular prism
2. Name the figure with 1 polygon base with a vertex opposite it, sides that are
triangular, and is names by the shape of its base.
a. cone
b. cylinder
c. pyramid
d. rectangular prism
3. Name the figure:
a. cone
b. cylinder
c. pentagonal pyramid
d. pyramid
4. Name the figure:
a. rectangular pyramid
b. box
c. rectangular prism
d. triangular prism
5. Which of the following is not true?
a. A polyhedron is a 3D figure.
b. A cone is a polyhedron.
c. A polyhedron cannot have sides that are not polyhedrons.
d. A polyhedron has faces that are all polygons.
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6. How many vertices does a cube have?
a. 8
b. 6
c. 12
d. 4
7. How many vertices does a square pyramid have?
a. 5
b. 6
c. 4
d. 8
8. How many faces does a square pyramid have?
a. 5
b. 6
c. 4
d. 8
9. How many faces does a triangular prism have?
a. 9
b. 6
c. 3
d. 5
10. How many edges does a cube have?
a. 8
b. 6
c. 12
d. 4
11. If a pentagonal pyramid has 6 faces and 6 vertices, how many edges does it have?
a. 0
b. 10
c. 12
d. 6
12. What is the labeling used when dealing with volume?
a. units2
b. units3
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13. What is the volume of the cube?
12 in
a. 36 in3
b. 1728 in3
c. 144 in3
d. 12 in3
14. What is the volume of the square pyramid?
a. 960 in3
b. 510 in3
c. 544 in3
d. 10,240 in3
15. What is the volume of the sphere?
a. 85.3 cm3
b. 268.1 cm3
c. 64 cm3
d. 201.1 cm3
16. What is the volume of the cone?
a. 15𝜋 ft3
b. 22.5𝜋 ft3
c. 45𝜋 ft3
d. 60𝜋 ft3
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3D Geometry Short Constructed Response Questions
17. What is the volume of a cylinder with a base area of 5𝜋 cm2 and a height of 15 cm?
Leave your answer in terms of 𝜋.
18. What is the volume of a triangular prism, with a height of 7 in, and a triangle base,
with a height of 4 in, and a base of 4 in?
19. A sphere with a radius of 3 ft is compared to a sphere with a radius of 6 ft. How
many times larger is the volume of the larger sphere compared to the volume of the
smaller sphere?
20. What is a possible length, width, and height for a rectangular prism whose volume is
112 cm3?
21. What is the volume of a hemisphere (half a sphere) with a diameter of 3.75 in? Use
the 𝜋 button on your calculator when calculating your answer.
22. What is the height of a cube with a volume of 343 ft3?
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23. What is the base area of a cone whose volume is 95in3 and has a height of 15 in?
24. List the number of vertices, edges, and faces contained in a pentagonal pyramid.
25. List the number of vertices, edges, and faces contained in a rectangular prism.
3D Geometry Extended Constructed Response Questions
26. A rectangular prism cereal box has a width of 3 inches, a height of 12 inches, and a
length of 6 inches.
a. What is the volume of the cereal box?
b. Draw the cereal box on graph paper.
c. A spherical bouncy ball is in the cereal box with a
diameter of 3 inches. What is the amount of volume in the
cereal box that the cereal has to fill? Use 3.14 as your
value of 𝜋.
27. A circular pool has a diameter of 40 feet and is surrounded by a concrete walkway
that has a width of 4 feet and a depth of 5 inches. What is the volume of the
concrete path? (write your final answer in feet)
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28. The figure shows a right circular cylinder & a sphere. The cylinder and sphere have
the same radius, and the height of the cylinder is equivalent to the diameter of the
sphere/cylinder.
9 cm
h
9 cm
a.
What is the height of the cylinder?
b.
Determine the volume for both solids. Leave your answers in terms of 𝜋.
c.
Determine the ratio that compares the volume of the cylinder to the volume of
the sphere.
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Answer Key
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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
96 ft3
942.48 in3
48 u3
60 m3
216 ft3
1099.56 cm3
180 in3
351.68 u3
180𝜋 in3
4 feet
628.32 ft3
69.12 ft3
1600𝜋 ft3
240 u3
180 ft3
226.19 mm3
84 m3
512 ft3
703.72 cm3
154 in3
254.47 u3
432𝜋 u3
3 feet
254.47 ft3
131.95 ft3
1875𝜋 ft3
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47.
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72.
40 u3
75.40 ft3
1436.76 cm3
40 cm3
84.82 u3
27 ft3
268.08 m3
96𝜋 cm3
50.24 ft3
142.90𝜋 in3
$0.08 per cubic inch
$6
a) 45 𝜋 ft3
b) 1:3
904.78 cm3
96 u3
414.69 ft3
64 cm3
134.04 u3
64 ft3
85.33𝜋 cm3
523.60 m3
8.37 ft3
126.43𝜋 in3
$0.32 per cubic inch
$12
a) 8𝜋 ft3
b) 1:3
Unit Review Answer Key
1. b
2. c
3. c
4. c
5. b
6. a
7. a
8. a
9. d
10. c
11. b
12. b
13. b
14. d
15. b
16. a
17. 75 𝜋 cm3
18. 56 in3
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19. 8 times larger
20. answers will vary
21. 13.81 in3
22. 7 ft
23. 19 in
24. 6 faces, 6 vertices, 10 edges
25. 6 faces, 8 vertices, 12 edges
26.
a. 216 inches3
b. graph paper model
c. 201.87 inches3
27. 230.38 feet3
28.
a) 18 cm
b) Cylinder: V = 1458 𝜋 cm3
Sphere: V = 972 𝜋 cm3
c) 3:2
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