8th Grade. Slide 1 / 97. Slide 2 / 97. Slide 3 / 97. 3D Geometry. Table of Contents. 3-Dimensional Solids. Volume. Glossary & Standards

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1 Slide 1 / 97 Slide 2 / 97 8th Grade 3D Geometry Table of Contents Slide 3 / 97 3-Dimensional Solids Click on the topic to go to that section Volume Prisms and Cylinders Pyramids, Cones & Spheres More Practice/ Review Glossary & Standards

2 Slide 4 / 97 3-Dimensional Solids Return to Table of Contents Slide 5 / 97 The following link will take you to a site with interactive 3-D figures and nets. Polyhedron Polyhedron A 3-D figure whose faces are all polygons. Sort the figures into the appropriate side. Slide 6 / 97 Polyhedron Not Polyhedron

3 3-Dimensional Solids Slide 7 / 97 Categories & Characteristics of 3-D Solids: Prisms 1. Have 2 congruent, polygon bases which are parallel to one another click to reveal 2. Sides are rectangular (parallelograms) 3. Named by the shape of their base Pyramids 1. Have 1 polygon base with a vertex opposite it 2. Sides are triangular click to reveal 3. Named by the shape of their base 3-Dimensional Solids Slide 8 / 97 Categories & Characteristics of 3-D Solids: Cylinders 1. Have 2 congruent, circular bases which are parallel to one click another to reveal 2. Sides are curved Cones 1. Have 1 circular bases with a vertex opposite it 2. Sides are curved click to reveal 3-Dimensional Solids Slide 9 / 97 Vocabulary Words for 3-D Solids: Polyhedron Face Edge A 3-D figure whose faces are all polygons (Prisms & Pyramids) Flat surface of a Polyhedron Line segment formed where 2 faces meet Vertex (Vertices) Point where 3 or more faces/edges meet

4 Sort the figures. If you are incorrect, the figure will be sent back. Slide 10 / 97 Slide 11 / 97 1 Name the figure. A B C D E F Rectangular Prism Triangular Pyramid Hexagonal Prism Rectangular Pyramid Cylinder Cone 2 Name the figure. Slide 12 / 97 A B C D E F Rectangular Pyramid Triangular Prism Octagonal Prism Circular Pyramid Cylinder Cone

5 3 Name the figure. Slide 13 / 97 A B C D E F Rectangular Pyramid Triangular Pyramid Triangular Prism Hexagonal Pyramid Cylinder Cone 4 Name the figure. Slide 14 / 97 A B C D E F Rectangular Prism Triangular Prism Square Prism Rectangular Pyramid Cylinder Cone 5 Name the figure. Slide 15 / 97 A B C D E F Rectangular Prism Triangular Pyramid Circular Prism Circular Pyramid Cylinder Cone

6 For each figure, find the number of faces, vertices and edges. Can you figure out a relationship between the number of faces, vertices and edges of 3-Dimensional Figures? Name Faces Vertices Edges Cube Rectangular Prism Triangular Prism Triangular Pyramid Square Pyramid Pentagonal Pyramid Octagonal Prism Math Practice Slide 16 / 97 Euler's Formula Slide 17 / 97 F + V = E + 2 Euler's Formula is the number of edges plus 2 is equal to the sum of the faces and vertices. 6 How many faces does a pentagonal prism have? Slide 18 / 97

7 7 How many edges does a rectangular pyramid have? Slide 19 / 97 8 How many vertices does a triangular prism have? Slide 20 / 97 9 How many faces does a hexagonal pyramid have? Slide 21 / 97

8 10 How many vertices does a triangular pyramid have? Slide 22 / 97 Slide 23 / 97 Volume Return to Table of Contents Volume Slide 24 / 97 Volume - The amount of space occupied by a 3-D Figure click to reveal - The number of cubic units needed to FILL a 3-D Figure (layering) Label - Units click 3 to or reveal cubic units

9 Volume Activity Slide 25 / 97 Click the link below for the activity. Lab #1: Volume Activity Slide 26 / 97 Volume of Prisms & Cylinders Return to Table of Contents Volume Slide 27 / 97 Volume of Prisms & Cylinders: Area of click Base to reveal x Height, or V = Bh Area Formulas: Rectangle = lw or bh click to reveal Triangle = bh or 2 click to reveal 1 2 (bh) Circle = πr 2 click to reveal

10 Find the Volume Slide 28 / 97 8 m 2 m 5 m Find the Volume Use 3.14 as your value of π. Slide 29 / 97 9 yd 10 yd Find the Volume Slide 30 / 97 A cylinder with a radius measuring 2 cm and a height of 5 cm is compared to a cylinder with a radius of 4 cm and a height of 5 cm. Amy says that the volume of the cylinder with a radius of 4 cm is double the volume of the cylinder with a radius of 2 cm. She used 3.14 as her value of π. Is she correct? Explain your reasoning. Start by calculating the volume of both cylinders. V = (3.14)(2) 2 (5) V = (3.14)(4)2 (5) V = 62.8 cm 3 V = cm 3 click Answer the question. click No, Amy is not correct. If the radius of the cylinder doubles, the volume does not double. Instead it quadruples. click

11 Slide 31 / 97 Teachers: Use this Mathematical Practice Pull Tab for the next 9 SMART Response slides. 11 Find the Volume. Slide 32 / 97 4 in in 1 12 in 12 Find the volume of a rectangular prism with length 2 cm, width 3.3 cm and height 5.1 cm. Slide 33 / 97

12 13 Which is a possible length, width and height for a rectangular prism whose volume = 18 cm 3 Slide 34 / 97 A 1 x 2 x 18 B 6 x 3 x 3 C 2 x 3 x 3 D 3 x 3 x 3 14 Find the volume. Slide 35 / ft 50 ft 42 ft 21 ft 15 A box-shaped refrigerator measures 12 by 10 by 7 on the outside. All six sides of the refrigerator are 1 unit thick. What is the inside volume of the refrigerator in cubic units? Slide 36 / 97 HINT: You may want to draw a picture!

13 16 Find the volume. Use 3.14 as your value of π. Slide 37 / m 6 m 17 Which circular glass holds more water? Slide 38 / 97 A B Glass A having a 7.5 cm diameter and standing 12 cm high Glass B having a 4 cm radius and a height of 11.5 cm Note: Use 3.14 as your value of π. 18 What is the volume of the largest cylinder that can be placed into a cube that measures 10 feet on an edge? Use 3.14 as your value of π. Slide 39 / 97

14 19 A circular garden has a diameter of 20 feet and is surrounded by a concrete border that has a width of three feet and a depth of 6 inches. What is the volume of concrete in the path? Use 3.14 as your value of π. Slide 40 / 97 Answer in Terms of π Slide 41 / 97 Sometimes, a question will ask you to "Leave your answer in terms of π". This means that you treat π like a variable & only do the arithmetic operations with the remaining numbers. Ex: If a cylinder has a radius of 3 and a height of 4, then Volume = π(3) 2 (4) = π(9)(4) = 36π units 2 Let's try some more problems like this one. Click here to return to cones & spheres. Find the Volume Slide 42 / 97 9 yd Leave your answer in terms of π. 10 yd

15 Find the Volume Slide 43 / 97 Leave your answer in terms of π. 15 ft 30 ft 20 A cylinder has a radius of 7 and a height of 2. What is its volume? Leave your answer in terms of π. Slide 44 / 97 A 14π units3 B 28π units3 C 49π units3 D 98π units3 21 A cylinder has a diameter of 12 in. and a height of 12 in. What is its volume? Leave your answer in terms of π. Slide 45 / 97 A 144π in 3 B 432π in 3 C 864π in 3 D 1,728π in 3

16 22 A cylinder has a diameter of 17 in. and a height of 5 in. What is its volume? Leave your answer in terms of π. Slide 46 / 97 A π in 3 B π in 3 C 425π in 3 D 1,228.25π in 3 23 A circular pool has a diameter of 40 feet and is surrounded by a wooden deck that has a width of 4 feet and a depth of 6 inches. What is the volume of the wooden deck? Leave your answer in terms of π. Slide 47 / 97 A 88π ft 3 B 176π ft 3 C 400π ft 3 D 576π ft 3 Slide 48 / 97 Volume of Pyramids, Cones & Spheres Return to Table of Contents

17 Slide 49 / 97 Slide 50 / 97 Demonstration comparing volume of Cones & Spheres with volume of Cylinders click to go to web site Volume of a Cone Slide 51 / 97 A cone is 1/3 the volume of a cylinder with the same base area (B) and height (h). 1 3 Area of Base x Height 3 click to reveal (Area of Base x Height) = = Bh 3 Bh 1 3

18 Volume of a Sphere Slide 52 / 97 A sphere is 2/3 the volume of a cylinder with the same base area (B) and height (h). click to reveal V = 2/3 (Volume of Cylinder) π V= 2/3 ( r 2 h ) or V = 4/3 πr 3 Volume Slide 53 / 97 How much ice cream can a Friendly s Waffle cone hold if it has a diameter of 6 in and its height is 10 in? Use 3.14 as your value of π. (Just Ice Cream within Cone. Not on Top) Volume and Mass used in portion control. $$$ 24 Find the volume. Use 3.14 as your value of π. Slide 54 / 97 9 in 4 in

19 25 Find the Volume. Use 3.14 as your value of π. Slide 55 / 97 8 cm 5 cm Volume Slide 56 / 97 If the radius of a sphere is 5.5 cm, what is its volume? Use 3.14 as your value of π. Click here 4 V = πr 3 3 V = 4 (3.14)(5.5) 3 3 V = cm 3 26 What is the volume of a sphere with a radius of 8 ft? Use 3.14 as your value of π. Slide 57 / 97

20 27 What is the volume of a sphere with a diameter of 4.25 in? Use 3.14 as your value of π. Slide 58 / 97 Volume in Terms of π Slide 59 / 97 Similar to when we found the volume of a cylinder, with a cone and a sphere, you could be asked to "Leave your answer in terms of π". Click here if you need to review that property. Volume in Terms of π Slide 60 / 97 You are selling lemonade in conic cups (cups shaped like cones). How much lemonade will each customer get to drink? Leave your answer in terms of π. 8 cm 11 cm

21 Volume in Terms of π Slide 61 / 97 If the radius of a sphere is 6 cm, what is its volume? Leave your answer in terms of π. 28 Find the volume of the cone below. Leave your answer in terms of π. Slide 62 / 97 A 12π in 3 B 36π in 3 9 in C 48π in 3 D 144π in 3 4 in 29 Find the volume of the sphere that has a diameter of 18 cm. Leave your answer in terms of π. Slide 63 / 97 A 729π cm 3 B 972π cm 3 C 5,832π cm 3 D 7,776π cm 3

22 30 Find the volume of the cone below. Leave your answer in terms of π. Slide 64 / 97 A 49π in 3 B 84π in 3 12 in C 147π in 3 D 252π in 3 7 in 31 Find the volume of a sphere that has a radius of 4.5 cm. Leave your answer in terms of π. Slide 65 / 97 A 27π cm 3 B π cm 3 C 121.5π cm 3 D 364.5π cm 3 32 A sphere with a radius measuring 9 cm is compared to a sphere with a radius of 18 cm. Jeff says that the volume of the sphere with a radius of 18 cm is double the volume of the sphere with a radius of 9 cm. Is he correct? Explain your reasoning. When you are done calculating your answer, type in the number "1". Slide 66 / 97

23 Volume of a Pyramid Slide 67 / 97 A pyramid is 1/3 the volume of a prism with the same base area (B) and height (h). Area of Base x Height 3 click to reveal 1 (Area of Base x Height) = 3 = Bh 3 Bh 1 3 Pyramids Slide 68 / 97 Pyramids are named by the shape of their base.. The volume is a pyramid is 1/3 the volume of a prism with the same base area(b) and height (h). 1 V = 3 Bh =5 m side length = 4 m V = 1 Bh 3 V = 1 (4)(4)(5) 3 V = 1 (80) 3 V = 26 2 m 3 3 Click here 33 Find the Volume of a triangular pyramid with a base edge of 8 in, base height of 4 in and a pyramid height of 10 in. Slide 69 / in 4 in 8 in

24 34 Find the volume. Slide 70 / cm 7 cm 8 cm Slide 71 / 97 More Practice / Review Return to Table of Contents 35 Find the volume. Slide 72 / mm 8 mm 15 mm

25 36 Find the volume of a rectangular pyramid with a base length of 2.7 meters and a base width of 1.3 meters, and the height of the pyramid is 2.4 meters. Slide 73 / 97 HINT: Drawing a diagram will help! 37 Find the volume of a square pyramid with base edge of 4 inches and pyramid height of 3 inches. Slide 74 / Find the Volume. Slide 75 / m 9 m 12 m 6 m 9 m

26 39 Find the Volume. Use 3.14 as your value of π. Slide 76 / ft 14 ft 40 Find the Volume. Use 3.14 as your value of π. Slide 77 / 97 8 in 6.9 in 41 Find the Volume. Slide 78 / 97 9 ft 4 ft 8 ft 7 ft

27 42 A cone 20 cm in diameter and 14 cm high was used to fill a cubical planter, 25 cm per edge, with soil. How many full cones of soil were needed to fill the planter? Slide 79 / cm 14 cm 25 cm 43 Find the Volume. Slide 80 / 97 9 in 9 in 2 in 7 in 8 in Name a 3-D Figure that is not a polyhedron. Slide 81 / 97

28 Name a 3-D figure that has 6 rectangular faces. Slide 82 / Find the volume. Slide 83 / m 80 m 40 m 45 The figure shows a right circular cylinder and a right circular cone. The cylinder and the cone have the same base and the same height. Slide 84 / 97 Part A: What is the volume of the cone, in cubic feet? A 12π ft 3 B 16π ft 3 C 36π ft 3 D 48π ft 3 From PARCC EOY sample test calculator #11

29 46 Part B: What is the ratio of the cone's volume to the cylinder's volume? Slide 85 / 97 Slide 86 / 97 Glossary & Standards Return to Table of Contents Cone Slide 87 / 97 A polyhedron that has one circular base with a vertex opposite of it and sides that are curved. curved surface ice cream cone pencil tip polyhedron traffic cone Back to Instruction

30 Cylinder Slide 88 / 97 A polyhedron that has two congruent circular bases which are parallel to one another and sides that are curved. curved surface candles Pringles can polyhedron pizza Back to Instruction Edge Slide 89 / 97 Line segment formed where 2 faces meet. A triangular pyramid has 6 edges. Back to Instruction Euler's Formula Slide 90 / 97 The number of edges plus 2 is equal to the sum of the faces and vertices. E + 2 = F + V pyramid: vertices = 4 faces = 4 E + 2= F + V E + 2 = E + 2 = 8 E = 6 Back to Instruction

31 Face Slide 91 / 97 Flat surface of a polyhedron. A triangular pyramid has 4 faces. (there is one you can't see) Back to Instruction Polyhedron Slide 92 / 97 A 3-D figure whose faces are all polygons. Cubes Prisms Pyramids Made of: Faces Edges Vertices Cylinders Cones Back to Instruction Prism A polyhedron that has two congruent, polygon bases which are parallel to one another, sides that are rectangular, and named by the shape of their base. Slide 93 / 97 Rectangular Prism Pentagonal Prism Triangular Pris m juice box body of pencil Block of cheese Back to Instruction

32 Pyramid Slide 94 / 97 A polyhedron that has one polygon base with a vertex opposite of it,sides that are triangular, and named by the shape of its base. Triangular Pyramid Square Pyramid Pentagonal Pyramid Back to Instruction Vertex Slide 95 / 97 Point where two or more straight lines/ faces/edges meet. A Corner. A triangular pyramid has 4 vertices. Back to Instruction Volume Slide 96 / 97 The amount of space occupied by a 3D figure. The number of cubic units needed to fill a 3D figure (layering). volume of prisms and cylinders: area of base x height V = area of base x h V = 2m x 5m x 8m V = 80m 3 Label: Units 3 or cubic units Back to Instruction

33 Standards for Mathematical Practices Slide 97 / 97 MP1 Make sense of problems and persevere in solving them. MP2 Reason abstractly and quantitatively. MP3 Construct viable arguments and critique the reasoning of others. MP4 Model with mathematics. MP5 Use appropriate tools strategically. MP6 Attend to precision. MP7 Look for and make use of structure. MP8 Look for and express regularity in repeated reasoning. Click on each standard to bring you to an example of how to meet this standard within the unit.