3 Dimensional Geometry Chapter Questions

  1. What are the differences between prisms and pyramids? Cylinders and cones?
  1. What is volume and how is it found?
  1. How are the volumes of cylinders, cones and spheres related?

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

Volume of Prisms and Cylinders

Class Work

Find the volume of each figure.

21.22.23.

24. A 5m x 3m x 4m rectangular prism

25. A cube with edge of 6ft

26. A cylinder with height of 14cm and base diameter of 10cm. Use the 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 8 and height 7. Use 3.14 as your value of .

29. A cylinder with a height of 5 in and a radius of 6 in. Leave your answer in terms of .

30. A box has volume of 24 ft3 and a base of 2 ft by 3ft, 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 .

Homework

Find the volume of each figure.

34.35.36.

37. A 6m x 7m x 2m rectangular prism

38. A cube with edges of 8ft

39. A cylinder with height of 14cm and base diameter of 8cm. Use the button on your calculator.

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 6 and height 9. Use the button on your calculator.

42. A cylinder with a radius of 6 and height 12. Leave your answer in terms of .

43. A box has volume of 24 ft3 and a base of 2 ft by 4ft, 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 .

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 cm2 and a height of 10cm.

51. A cone with base circumference of 6 and height 9. Use the 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 8m. Use the 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 .

55. A cone with radius 4 ft and a height of 36 inches. Use 3.14 as your value of .

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 .

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?

59. The figure shows a right circular cylinder & a right circular cone. The cylinder and cone have the same base and the same height.

a) What is the volume of the cylinder, in cubic feet? Leave your answer in terms of .

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 12cm.

64. A cone with base circumference of 8 and height 8. Use the 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 .

67. A sphere with a diameter of 10m. Use the button on your calculator.

68. A cone with radius 2 ft and a height of 24 inches. Use 3.14 as your value of .

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 .

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.

a) What is the volume of the cone, in cubic feet? Leave your answer in terms of .

b) What is the ratio of the cone’s volume to the cylinder’s volume?

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

  1. 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

  1. 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

  1. 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.

  1. How many vertices does a cube have?

a. 8

b. 6

c. 12

d. 4

  1. How many vertices does a square pyramid have?

a. 5

b. 6

c. 4

d. 8

  1. How many faces does a square pyramid have?

a. 5

b. 6

c. 4

d. 8

  1. How many faces does a triangular prism have?

a. 9

b. 6

c. 3

d. 5

  1. How many edges does a cube have?

a. 8

b. 6

c. 12

d. 4

  1. If a pentagonal pyramid has 6 faces and 6 vertices, how many edges does it have?

a. 0

b. 10

c. 12

d. 6

  1. What is the labeling used when dealing with volume?

a. units2

b. units3

  1. What is the volume of the cube?

a. 36 in3

b. 1728 in3

c. 144 in3

d. 12 in3

  1. What is the volume of the square pyramid?

a. 960 in3

b. 510 in3

c. 544 in3

d. 10,240 in3

  1. What is the volume of the sphere?

a. 85.3 cm3

b. 268.1 cm3

c. 64 cm3

d. 201.1 cm3

  1. What is the volume of the cone?

a. 15 ft3

b. 22.5 ft3

c. 45 ft3

d. 60 ft3

3D Geometry Short Constructed Response Questions

  1. What is the volume of a cylinder with a base area of 5 cm2 and a height of 15 cm? Leave your answer in terms of .
  1. 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?
  1. 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?
  1. What is a possible length, width, and height for a rectangular prism whose volume is 112 cm3?
  1. What is the volume of a hemisphere (half a sphere) with a diameter of 3.75 in? Use the button on your calculator when calculating your answer.
  1. What is the height of a cube with a volume of 343 ft3?
  1. What is the base area of a cone whose volume is 95in3 and has a height of 15 in?
  1. List the number of vertices, edges, and faces contained in a pentagonal pyramid.
  1. List the number of vertices, edges, and faces contained in a rectangular prism.

3D Geometry Extended Constructed Response Questions

  1. A rectangular prism cereal box has a width of 3 inches, a height of 12 inches, and a length of 6 inches.
  2. What is the volume of the cereal box?
  1. Draw the cereal box on graph paper.
  1. 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 .
  1. 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)
  1. 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.

  1. What is the height of the cylinder?
  1. Determine the volume for both solids. Leave your answers in terms of .
  1. Determine the ratio that compares the volume of the cylinder to the volume of the sphere.

Answer Key

NJ Center for Teaching and Learning ~ 1 ~

  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. 96 ft3
  22. 942.48 in3
  23. 48 u3
  24. 60m3
  25. 216 ft3
  26. 1099.56 cm3
  27. 180 in3
  28. 351.68 u3
  29. 180 in3
  30. 4 feet
  31. 628.32 ft3
  32. 69.12 ft3
  33. 1600 ft3
  34. 240 u3
  35. 180 ft3
  36. 226.19 mm3
  37. 84 m3
  38. 512 ft3
  39. 703.72 cm3
  40. 154 in3
  41. 254.47 u3
  42. 432 u3
  43. 3 feet
  44. 254.47 ft3
  45. 131.95 ft3
  46. 1875 ft3
  47. 40 u3
  48. 75.40 ft3
  49. 1436.76 cm3
  50. 40 cm3
  51. 84.82 u3
  52. 27 ft3
  53. 268.08 m3
  54. 96 cm3
  55. 50.24 ft3
  56. 142.90 in3
  57. $0.08 per cubic inch
  58. $6
  59. a) 45 ft3
    b) 1:3
  60. 904.78 cm3
  61. 96 u3
  62. 414.69 ft3
  63. 64 cm3
  64. 134.04 u3
  65. 64 ft3
  66. 85.33 cm3
  67. 523.60 m3
  68. 8.37 ft3
  69. 126.43 in3
  70. $0.32 per cubic inch
  71. $12
  72. a) 8 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

  1. a
  2. 75 cm3
  3. 56 in3

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 cm3

Sphere: V = 972 cm3

c) 3:2

NJ Center for Teaching and Learning ~ 1 ~