3D Geometry: Chapter Questions
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1 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?
2 3D Geometry: Chapter Problems 3 Dimensional Solids Class Work In 1-5, name the figure In 6-10, give the number faces, edges, and vertices of each shape triangular pyramid 10. square prism Homework In 11-15, name the figure In 16-20, give the number faces, edges, and vertices of each shape octagonal pyramid 20. rectangular prism
3 Cross Sections of 3-Dimensional Figures Class Work In 21-24, sketch the cross-section formed by cutting each figure horizontally In 25-28, sketch the cross-section formed by cutting each figure vertically. 25. Figure #1 Above 26. Figure #2 Above 27. Figure #3 Above 28. Figure #4 Above Homework In 29-33, sketch the cross-section formed by cutting each figure horizontally In 33-36, sketch the cross-section formed by cutting each figure vertically. 33. Figure #29 Above 34. Figure #30 Above 35. Figure #31 Above 36. Figure #32 Above
4 Volume of Prisms and Cylinders Class Work Find the volume of each figure 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 A box has volume of 24 ft 3 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 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 A box has volume of 24 ft 3 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?
5 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 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 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 A pentagonal pyramid with base area of 16 cm 2 and a height of 12 cm. 73. A cone with base circumference of 8π and height 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?
6 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 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
7 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 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?
8 Homework Find the surface area of the given figure 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
9 117. 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 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
10 133. Find the surface area of a sphere if its volume is 36π cm 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 Find the surface area of a sphere if its volume is 288π cm If the circumference of a soccer ball is 62.8 cm, what is its surface area?
11 Multiple Choice 1. How many edges are in a Rectangular Prism? a. 6 b. 15 c. 12 d Name the figure: a. Rectangular Pyramid b. Triangular Prism c. Rectangular Prism d. Triangular Pyramid UNIT REVIEW 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 m 3 b m 3 c m 3 d m 3 5. A triangular pyramid has a base with area 12 ft 2 and a height of 5 ft, what is the volume of the pyramid? a. 24 ft 3 b. 30 ft 3 c. 60 ft 3 d. Cannot be determined 6. How many vertices are in an rectangular prism? a. 6 b. 8 c. 10 d A square pyramid has base edges of 0.3 mm and a height of 10 cm, what is its volume? a. 3.0 cm 3 b. 9.0 mm 3 c. 30 mm 3 d. 900 mm 3
12 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 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 Which figure(s) has a square for its vertical cross section? a. b. c. d. 11. What is volume of the given figure? a ft 2 b ft 2 c ft 2 d ft 2 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 in 2 b in 2 c in 2 d in What is the surface area? a. 176 cm 2 b cm 2 c cm 2 d cm 2
13 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 ft 3 of water weighs 62.4 lbs? 15. The volume of the cone, with a radius of 3 in, is 160 in 3. 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?
14 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/in 2 for the label, what is the profit for each can of broth sold?
15 Answer Key 1. Hexagonal Prism 2. Cylinder 3. Octagonal Prism 4. Cone 5. Pentagonal Pyramid 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 faces, 8 vertices, 12 edges 11. Triangular Pyramid 12. Cylinder 13. Triangular Prism 14. Pentagonal Prism 15. Cone faces, 4 vertices, 6 edges faces, 6 vertices, 9 edges faces, 10 vertices, 15 edges faces, 9 vertices, 16 edges 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 ft in u m ft cm in u feet ft ft u ft mm m ft cm in u feet ft ft u ft cm cm u ft m ft $0.08 per cubic inch 68. $ cm u ft cm u ft m ft $0.32 per cubic inch 78. $ m² cm² cm² in² ft² cm² gallons in² ft² in² cm² cm² m² cm² gallons
16 in² in² in² in² in² in² in² 101. Square pyramid with base edges of 10 mm and slant height of 8 mm is greater (260 mm²) ,920 ft² in² in² in² in² in² in² times greater (864 m² / 156 m²) ,155 ft² ft² in² cm² cm² m² cm² in² 118. Cylinder with radius of 6 in and height of 4 in is greater by in² cm² m² cm² mm² cm² in² in² 126. Cylinder with radius of 10 in and height of 6 in is greater by in² km² ft² ft² ft² in² km² cm² ,288,000 square miles ft² in² ft² km² mm² mm² cm² 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 LBS IN 16. HORIZONTAL: 4 X 6 VERTICAL: 8 X CM ,120 IN A IN 3 B IN 2 C IN 2 D. APPROXIMATELY 40 CENTS
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