3 Dimensional Geometry Chapter Questions. 1. What are the differences between prisms and pyramids? Cylinders and cones?

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1 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? NJ Center for Teaching and Learning ~ 1 ~

2 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 NJ Center for Teaching and Learning ~ 2 ~

3 Volume of Prisms and Cylinders Class Work Find the volume of each figure 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 ft 3 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 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. NJ Center for Teaching and Learning ~ 3 ~

4 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 ft 3 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 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? NJ Center for Teaching and Learning ~ 4 ~

5 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 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 ft 63. A pentagonal pyramid with base area of 16 cm 2 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. NJ Center for Teaching and Learning ~ 5 ~

6 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? NJ Center for Teaching and Learning ~ 6 ~

7 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. 3. Name the figure: a. cone b. cylinder c. pyramid d. rectangular prism 4. Name the figure: a. cone b. cylinder c. pentagonal pyramid d. pyramid 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. NJ Center for Teaching and Learning ~ 7 ~

8 6. How many vertices does a cube have? a. 8 b. 6 c. 12 d How many vertices does a square pyramid have? a. 5 b. 6 c. 4 d How many faces does a square pyramid have? a. 5 b. 6 c. 4 d How many faces does a triangular prism have? a. 9 b. 6 c. 3 d How many edges does a cube have? a. 8 b. 6 c. 12 d If a pentagonal pyramid has 6 faces and 6 vertices, how many edges does it have? a. 0 b. 10 c. 12 d What is the labeling used when dealing with volume? a. units 2 b. units 3 NJ Center for Teaching and Learning ~ 8 ~

9 13. What is the volume of the cube? 12 in a. 36 in 3 b in 3 c. 144 in 3 d. 12 in What is the volume of the square pyramid? a. 960 in 3 b. 510 in 3 c. 544 in 3 d. 10,240 in What is the volume of the sphere? a cm 3 b cm 3 c. 64 cm 3 d cm What is the volume of the cone? a. 15π ft 3 b. 22.5π ft 3 c. 45π ft 3 d. 60π ft 3 5 ft NJ Center for Teaching and Learning ~ 9 ~ 3 ft

10 3D Geometry Short Constructed Response Questions 17. What is the volume of a cylinder with a base area of 5π cm 2 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 cm 3? 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 ft 3? NJ Center for Teaching and Learning ~ 10 ~

11 23. What is the base area of a cone whose volume is 95in 3 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) NJ Center for Teaching and Learning ~ 11 ~

12 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. NJ Center for Teaching and Learning ~ 12 ~

13 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 ft in u m ft cm in u π in feet ft ft π ft u ft mm m ft cm in u π u feet ft ft π ft u ft cm cm u ft m π cm ft π in $0.08 per cubic inch 58. $6 59. a) 45 π ft 3 b) 1: cm u ft cm u ft π cm m ft π in $0.32 per cubic inch 71. $ a) 8π ft 3 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 π cm in 3 NJ Center for Teaching and Learning ~ 13 ~

14 19. 8 times larger 20. answers will vary in ft in faces, 6 vertices, 10 edges faces, 8 vertices, 12 edges 26. a. 216 inches 3 b. graph paper model c inches feet a) 18 cm b) Cylinder: V = 1458 π cm 3 Sphere: V = 972 π cm 3 c) 3:2 NJ Center for Teaching and Learning ~ 14 ~

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