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Algebra / Geometry III: Unit 5- 3-D GeometrySUCCESS CRITERIA:

1. Be able calculate the lateral area, surface area, and volume for prisms, pyramids, cylinders and cones.

2. Be able calculate the surface area and volume of a sphere.

3. Be able to use the concepts of lateral area, surface area, and/or volume to solve real-world application problems.

INSTRUCTOR: Craig Sherman

Hidden Lake High SchoolWestminster Public Schools

PMI-NJ Center for Teaching & Learning ~1~ NJCTL.org

EMPOWER Recorded TARGET SCALE THEME

MA.11.G.02.04 Identify Cross-Sections

MA.11.G.03.04 Geometric Modeling

MA.11.G.06.04 Areas & Volumes of 3-D Figure

PROFICIENCY SCALE:

SCORE REQUIREMENTS

4.0 In addition to exhibiting Score 3.0 performance, in-depth inferences and applications that go BEYOND what was taught in class.

Score 4.0 does not equate to more work but rather a higher level of performance.3.5 In addition to Score 3.0 performance, in-depth inferences and applications with partial success.

3.0 The learner exhibits no major errors or omissions regarding any of the information and processes (simple or complex) that were explicitly taught.

o Use the properties of exponents to simplify an expression, ANDo Perform numeric operations to simplify a polynomial expression, ANDo Graph polynomial equations and identify its key features, ANDo Identify roots to a polynomial equation through graphs and factoring, ANDo Write polynomial equations using its zeros.

2.0 Can do one or more of the following skills / concepts: There are no major errors or omissions regarding the simpler details and processes as the learner…

o Use the properties of exponents to simplify an expression, ORo Add, Subtract, and multiply polynomial expressions, ORo Factor polynomial expression, ORo Divide a polynomial expression using synthetic division ORo Identify key characteristics of a polynomial graph, ORo Find the zeros(roots) of a polynomial equation by factoring, ORo Write a polynomial equation using its roots(zeros).

1.0 Know and use the vocabulary Identify the Basic Elements

With help, a partial understanding of some of the simpler details and process

PMI-NJ Center for Teaching & Learning ~2~ NJCTL.org

Surface Area of a PrismClass Work1. A jewelry store buys small boxes in which to wrap items that they sell. The diagram below shows one of

the boxes. Find the lateral area and the surface area of the box to the nearest whole number.

2. Find the lateral area and surface area of the hexagonal prism.

3. Find the surface area of the composite space figure.

4. Consider the prism shown below.

a. Draw a net for the prism and label all dimensions.

b. Use the net to find the surface area of the prism.

5. Find the lateral area and surface area of the triangular prism.a. b. c.

Algebra/Geometry III – 3D Geometry ~3~ NJCTL.org

Homework6. Draw the net and label all of the dimensions for the prism. Find the lateral area and surface area of the

rectangular prism.

7. Find the lateral area and surface area of the regular pentagonal prism.

8. Find the surface area of the composite space figure.A 5x6x8 box with a triangular prism removed.(Triangle is equilateral)

9. Find the lateral area and surface area of the triangular prisms.a b.


Surface Area of a CylinderClass Work10. The radius of the base of a cylinder is 39 in. and its height is 33 in. Find the surface area of the cylinder in

terms of .

11. Find the Lateral Area and Surface Area of the Cylinder

12. Find the surface area of the composite figure.

PARCC-type Questions: 13. Andrew is planning to cover the lateral surface of a large cylindrical garbage can with decorative fabric for a

theme party. The can has a diameter of 3 feet and a height of 3.5 feet. How much fabric does he need if he covers the lid but not the bottom of the can?

14. Jalissa wants to paint just the sides of a cylindrical pottery vase that has a height of 35 cm and a diameter of 12 cm. Find the number of square centimeters she will need to paint. Explain the method you would use to find the lateral area.

15. A washer is a cylindrical solid with a smaller cylinder removed from the center and then dipped in a special coating. If the diameter of the washer is 4”, the diameter of the hole is 1“, and height ¼ “, find the surface area of the washer.


Homework16. Find the Lateral Area and Surface Area of the Cylinder a b.

17. Find the surface area for the composite figure.

PARCC-type Questions:18. Andrew is planning to cover the lateral surface of a large cylindrical swimming pool with decorative fabric

for a theme party. The pool has a radius of 9 feet and a height of 4 feet. How much fabric does he need?

19. Jasmin wants to paint just the sides of a cylindrical pottery vase that has a height of 48 cm and a diameter of 19 cm. Find the number of square centimeters she will need to paint.

20. A washer is a cylindrical solid with a smaller cylinder removed from the center and then dipped in a special coating. If the diameter of the washer is 3”, the diameter of the hole is ½“, and height is ¼ “, find the surface area of the washer.


Surface Area of a PyramidClass Work21. Find the surface area of the pyramid.

22. Find the slant height, lateral area and surface area of the pyramid.

23. Find the slant height, lateral area and surface area of each square pyramid. a. b.

24. Find the surface area of the pyramid shown below.

25. Find the surface area of the composite figure.

26. A rectangular pyramid fits exactly on top of a rectangular prism. The prism has a length of 15 cm, a width of 5 cm, and a height of 7 cm. The pyramid has a height of 13 cm. Find the surface area of the composite figure.


Homework27. A regular hexagonal pyramid has base edges of 48 cm and a slant height of 26 cm. Find the lateral area

and surface area.

28. Find the slant height, lateral area and surface area of each square pyramid. a. b.

29. Find the surface area of the pyramid shown below. The base of the pyramid is a regular octagon.

30. Find the Surface Area of the composite figure.


Surface Area of a ConeClass Work31. Find the slant height of the cone.

32. Find the surface area of the cone in terms of . a. b.

33. Find the surface area of a conical grain storage tank that has a height of 30 meters and a diameter of 14 meters.

34. The lateral area of a right cone is 40π ft2, find the height of the cone if slant height is 10ft.

35. The surface area of a right cone is 55π cm2, find the radius if the slant height is 6cm.

Homework36. Find the slant height of the cone with height 7 and radius 6.

37. Find the Lateral Area and surface Area of the cone. a. b.

38. The lateral area of a cone is 558 cm2. The radius is 31 cm. Find the slant height.

39. The lateral area of a right cone is 30π ft2, find the height of the cone if slant height is 8ft.

40. The surface area of a right cone is 30π cm2, find the radius if the slant height is 7cm.


Volume of PrismsClass Work41. Concrete can be purchased by the cubic yard. How much will it cost to pour a slab 18 feet by 18 feet by 4

inches for a patio if the concrete costs $41.00 per cubic yard?

42. Find the volume of the rectangular prisma. b.

43. Find the volume of the triangular prisma. b. c.

44. Find the volume.a. b.


Homework45. A jewelry store buys small boxes in which to wrap items that they sell. The diagram below shows one of the

boxes. Find the volume of the box.

46. Find the volume of the Rectangular Prism.

47. Find the volume of the box w/ triangular prism removed.

48. Find the volume of the Triangular Prisma. b.

49. Find the volume.


Volume of CylindersClass Work50. The radius of the base of a cylinder is 39 in. and its height is 33 in. Find the volume of the cylinder.

51. A cylinder has a volume of 271.4 cubic inches and a base diameter of 12 in. Find the height of the cylinder.

52. Find the volume of the cylinder.

53. Find the volume of the composite figure.

54. Denise wants to use a cylindrical garbage can for recycling. The can has a diameter of 4 feet and a height of 2.5 feet. How many cubic feet of recycling will fit into the garbage can?

55. A washer is a cylindrical solid with a smaller cylinder removed from the center. The diameter of the washer is 3”, the diameter of the hole is ½”, and height ¼ “. Find the volume of the washer.

Homework

56. Find the volume of the cylinder. a. b.


58. Denise is going to a potluck dinner party and needs to use a cylindrical container for her potato salad. The container has a diameter of 15 inches and a height of 7 inches. How many cubic inches of potato salad can Denise fit into the container to take to the pot luck dinner?

59. A washer is a cylindrical solid with a smaller cylinder removed from the center. If the diameter of the washer is 4” and the diameter of the hole is 1“, and height ¼ “, find the volume of the washer.


Volume of PyramidsClass Work60. Find the volume of the pyramid.

a. b.


62. A rectangular pyramid fits exactly on top of a rectangular prism. The prism has a length of 15 cm, a width of 5 cm, and a height of 7 cm. The pyramid has a height of 13 cm. Find the volume of the composite figure.

PARCC-type Question:

63. The table shows the approximate measurements of the Pyramid of the Sun in Mexico and the Bent Pyramid in Egypt.

Pyramid Length (meters) Width (meters) Height (meters)Pyramid of the Sun 225 225 75

Bent Pyramid 188.6 188.6 101.1Approximately, what is the difference between the volume of the Pyramid of the Sun and the volume of the Bent Pyramid?a. 68,103 cubic metersb. 105,582 cubic metersc. 200,752 cubic metersd. 7,392,998 cubic meters


Homework64. A square pyramid has base edges of 48 cm and a slant height of 26 cm. Find its volume.

65. Find the volume of the pyramid.a. b.


67. A rectangular pyramid fits exactly on top of a rectangular prism. The prism has a length of 12 cm, a width of 6 cm, and a height of 8 cm. The pyramid has a height of 10 cm. Find the volume of the composite figure.

PARCC-type Question:

68. The table shows the approximate measurements of the two notable pyramid shaped buildings in the United States: the Luxor Hotel in Las Vegas, Nevada and the Pyramid Arena in Memphis, Tennessee.

Pyramid Length (feet) Width (feet) Height (feet)Luxor Hotel 600 600 350

Pyramid Arena 591 591 321Approximately, what is the difference between the volume of the Luxor Hotel and the volume of the Pyramid Arena?a. 1,123,804 cubic feetb. 4,626,933 cubic feetc. 13,880,799 cubic feetd. 79,373,067 cubic feet


Volume of ConesClass Work69. Find the volume of the cone in terms of . a. b. c.

70. A conical grain storage tank has a height of 30 meters and a diameter of 14 meters. Find the capacity of the storage tank. Round the answer to the nearest square meter.

71. If a cone has height 6 ft and volume 54 ft3, find the radius of the base.

72. The vertex of a right cone has a 20o angle and the slant height is 10 cm. Find the volume of the cone.

PARCC-type Question

73. Geometryville Farms is building a silo to store the grain that has a cylindrical base and a cone-shaped top. The laws of Geometryville say that the silo must have a maximum width of 18 feet and a maximum height of 25 feet.

Truck cars are used to transport the grain in loads that are 9 feet tall, 8 feet wide and 27.25 feet long. Geometryville wants to be able to store 3 truckloads of grain. Determine the height of the cylinder, h1, and the height of the cone, h2, that Geometryville Farms should use in the design. Show that your design will be able to store at least 3 truckloads of grain.


Homework74. The lateral area of a cone is 558 cm2. The radius is 5 cm. Find the volume of the cone to the nearest

tenth.

75. Find the volume of the cone.

76. If a cone has height 9 ft and volume 75 ft3, find the radius of the base.

77. The vertex of a right cone has a 40o angle and the slant height is 12 cm. Find the volume of the cone.

PARCC-type Question

78. Geometryville Farms is building a silo to store the food that has a cylindrical base and a cone-shaped top. The silo must have a maximum width of 16 feet and a maximum height of 22 feet.

Truck cars are used to transport the food in loads that are 9 feet tall, 8 feet wide and 27.25 feet long. Geometryville wants to be able to store 2 truckloads of food. Determine the height of the cylinder, h1, and the height of the cone, h2, that Geometryville Farms should use in the design. Show that your design will be able to store at least 2 truckloads of food.


Surface Area & Volume of SpheresClass Work79. The equator of Earth is approximately 25,000 miles. What is the diameter of the Earth?

80. The cross section of a sphere taken 4 units from the center of the sphere has radius 6. What is the radius of the sphere?

81. The cross section of a sphere taken 7 units from the center of the sphere has an area of 9πu2. What is the radius of the sphere?

82. A new dome-shaped storage shed is a hemisphere with height 10 yds. What is the area of the floor space?

83. A basketball has a circumference of 28”, what is the diameter of the ball?

84. Find the surface area of the sphere with the given dimension. a. Radius = 60 m b. Diameter = 24 cm c. Circumference = 13 mm

85. Find the surface area of a sphere that has a great circle with circumference of 13 mm. Round to the nearest tenth.

86. A balloon has a surface area of 200 cm2. Find the radius of the balloon.


87. Find the surface area of the sphere. a. b.

88. Three balls are packaged in a cylindrical container as shown below. The balls just touch the top, bottom, and sides of the cylinder. The diameter of each ball is 7 cm.a. What is the radius of the cylinder?

b. What is the height of the cylinder?

c. What is the total surface area of the three balls?

89. Find the volume of the sphere with the given dimension. Leave your answer in terms of .a. Radius = 60 m b. Diameter = 14 cm c. Circumference = 13 mm

90. A balloon has a surface area of 200 cm2. Find the volume of the balloon.

91. Find the volume of the sphere. a. b.

92. Three balls are packaged in a cylindrical container as shown below. The balls just touch the top, bottom, and sides of the cylinder. The diameter of each ball is 7 cm.a. What is the volume of the cylinder? Explain your method for finding the volume.

b. What is the total volume of the three balls? Explain your method for finding the total volume.

c. What percent of the volume of the container is occupied by the three balls? Explain how you would find the percent.


Homework93. The diameter of Jupiter is approximately 89,000 miles. How long is Jupiter’s equator?

94. The cross section of a sphere taken 8 units from the center of the sphere has radius 7. What is the radius of the sphere?

95. The cross section of a sphere taken 5 units from the center of the sphere has an area of 6u2. What is the radius of the sphere?

96. A new dome-shaped storage shed is a hemisphere with height 8 yds. What is the area of the floor space?

97. A baseball has a circumference of 9”, what is the diameter of the ball?

98. Find the surface area of the sphere with the given dimension. Leave your answer in terms of .a. Radius = 45 m b. Diameter = 16 cm c. Circumference = 27 mm

99. A ball has a surface area of 35.5 cm2. Find its radius.

100. Find the surface area of the sphere. a. b.

101. Three balls are packaged in a cylindrical container as shown below. The balls just touch the top, bottom, and sides of the cylinder. The diameter of each ball is 9 cm.a. What is the radius of the cylinder?

b. What is the height of the cylinder?

c. What is the total surface area of the three balls?


102. Find the volume of the sphere with the given dimension. Leave your answer in terms of .a. Radius = 45 m b. Diameter = 16 cm c. Circumference = 27 mm

133.

119. A ball has a volume of 15.5 cm3. Find the ball’s surface area.

120. Find the volume of the sphere. a. b.

121. Three balls are packaged in a cylindrical container as shown below. The balls just touch the top, bottom, and sides of the cylinder. The diameter of each ball is 13 cm.

a. What is the volume of the cylinder? Explain your method for finding the volume.

b. What is the total volume of the three balls? Explain your method for finding the total volume.

c. What percent of the volume of the container is occupied by the three balls? Explain how you would find the percent.


Review: 3-D Geometry

1. A right square pyramid has base edges of 6 and a height of 5. Find the slant height.a. 3.3b. 4c. 5.8d. 7.8

2. How many base edges does an oblique hexagonal prism have?a. 6b. 7c. 12d. 14

3. Find the number of vertices in the polyhedron if it contains 20 triangular faces and 12 pentagonal faces. a. 30b. 32c. 60d. 120

4. Find the lateral area of the right regular pyramid represented by the net.

5. The surface area of a box with length 5 cm and width 4 cm is 76 cm2. Find the height.

6. Find the surface area of a right cone with radius 3 and slant height 4.

7. A cross-section of a sphere, which is 6 units form the center of the sphere, has a circumference of 8π units. Find the surface area of the sphere.

8. Find the volume of the right triangular prism.


9. Find the volume of the cylinder with height 6 ft and radius 4 ft.

10. Find the volume of the right square pyramid with base edges of 8 and slant height of 10.

11. The surface areas of 2 similar spheres have the ratio of 9 to 4. If the volume of the larger sphere is 405 u3, what is the volume of the smaller sphere?

a. 120 u3

b. 160 u3

c. 180 u3

d. 270 u3

12. Find the surface area and volume of the composite figure below if the cone has a slant height of 10 inches, radius of 6 inches, and the cylinder has the same height as the cone.

13. In Geometryville’s Pentagon Park, they have a play tunnel shown in the figure below. It has a diameter length of 42 inches and a height of 14 feet. This year, Geometryville will hire some workers to paint the outside of the play tunnel with 3 new coats of paint. How much paint do the workers need?

Extended Constructed Response14. The Geometryville Aquarium is building a new tank space for its Pacific fish shown in the figure below. The

laws say that the dimensions of the tank must have a maximum length of 16 feet, a maximum width of 12 feet and a maximum height of 18 feet.


Salt water comes in cylindrical containers that measure 10 feet high and have a diameter of 8 feet. Determine the heights of the aquarium that should be used in the design. Show that your design will be able to store at least 4 cylindrical containers of water.


€¦ · web viewthe laws say that the dimensions of the tank must have a maximum length of 16...

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