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?

Answer Key

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