Slide 1 / 97 Slide 2 / 97 8th Grade 3D Geometry 2015-11-20 www.njctl.org Slide 3 / 97 Table of Contents Click on the topic to 3-Dimensional Solids go to that section Volume Prisms and Cylinders · Pyramids, Cones & Spheres · More Practice/ Review Glossary & Standards
Slide 3 (Answer) / 97 Table of Contents Click on the topic to 3-Dimensional Solids go to that section Volume Prisms and Cylinders · Vocabulary Words are bolded Teacher Notes Pyramids, Cones & Spheres · in the presentation. The text box the word is in is then More Practice/ Review linked to the page at the end of the presentation with the Glossary & Standards word defined on it. [This object is a pull tab] 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.
Slide 6 / 97 Polyhedron Polyhedron A 3-D figure whose faces are all polygons. Sort the figures into the appropriate side. Polyhedron Not Polyhedron Slide 7 / 97 3-Dimensional Solids 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 Slide 8 / 97 3-Dimensional Solids Categories & Characteristics of 3-D Solids: Cylinders 1. Have 2 congruent, circular bases which are parallel to one another click to reveal 2. Sides are curved Cones 1. Have 1 circular bases with a vertex opposite it 2. Sides are curved click to reveal
Slide 9 / 97 3-Dimensional Solids Vocabulary Words for 3-D Solids: Polyhedron A 3-D figure whose faces are all polygons (Prisms & Pyramids) Face Flat surface of a Polyhedron Edge Line segment formed where 2 faces meet Vertex (Vertices) Point where 3 or more faces/edges meet Slide 10 / 97 Sort the figures. If you are incorrect, the figure will be sent back. Slide 11 / 97 1 Name the figure. A Rectangular Prism B Triangular Pyramid C Hexagonal Prism D Rectangular Pyramid E Cylinder F Cone
Slide 11 (Answer) / 97 1 Name the figure. A Rectangular Prism B Triangular Pyramid Answer C Hexagonal Prism D D Rectangular Pyramid E Cylinder F Cone [This object is a pull tab] Slide 12 / 97 2 Name the figure. A Rectangular Pyramid B Triangular Prism C Octagonal Prism D Circular Pyramid E Cylinder F Cone Slide 12 (Answer) / 97 2 Name the figure. A Rectangular Pyramid B Triangular Prism Answer C Octagonal Prism E D Circular Pyramid E Cylinder F Cone [This object is a pull tab]
Slide 13 / 97 3 Name the figure. A Rectangular Pyramid B Triangular Pyramid C Triangular Prism D Hexagonal Pyramid E Cylinder F Cone Slide 13 (Answer) / 97 3 Name the figure. A Rectangular Pyramid B Triangular Pyramid Answer C Triangular Prism B D Hexagonal Pyramid E Cylinder F Cone [This object is a pull tab] Slide 14 / 97 4 Name the figure. A Rectangular Prism B Triangular Prism C Square Prism D Rectangular Pyramid E Cylinder F Cone
Slide 14 (Answer) / 97 4 Name the figure. A Rectangular Prism B Triangular Prism Answer C Square Prism A D Rectangular Pyramid E Cylinder F Cone [This object is a pull tab] Slide 15 / 97 5 Name the figure. A Rectangular Prism B Triangular Pyramid C Circular Prism D Circular Pyramid E Cylinder F Cone Slide 15 (Answer) / 97 5 Name the figure. A Rectangular Prism B Triangular Pyramid Answer C Circular Prism F D Circular Pyramid E Cylinder F Cone [This object is a pull tab]
Slide 16 / 97 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? Faces Vertices Edges Name 8 12 Cube 6 Rectangular 6 8 12 Math Practice Prism Triangular 5 6 9 Prism Triangular 4 4 6 Pyramid Square 5 5 8 Pyramid Pentagonal 6 6 10 Pyramid Octagonal 10 16 24 Prism Slide 17 / 97 Euler's Formula F + V = E + 2 Euler's Formula is the number of edges plus 2 is equal to the sum of the faces and vertices. Slide 18 / 97 6 How many faces does a pentagonal prism have?
Slide 18 (Answer) / 97 6 How many faces does a pentagonal prism have? Answer 7 [This object is a pull tab] Slide 19 / 97 7 How many edges does a rectangular pyramid have? Slide 19 (Answer) / 97 7 How many edges does a rectangular pyramid have? Answer 8 [This object is a pull tab]
Slide 20 / 97 8 How many vertices does a triangular prism have? Slide 20 (Answer) / 97 8 How many vertices does a triangular prism have? Answer 6 [This object is a pull tab] Slide 21 / 97 How many faces does a hexagonal pyramid have? 9
Slide 21 (Answer) / 97 How many faces does a hexagonal pyramid have? 9 Answer 7 [This object is a pull tab] Slide 22 / 97 10 How many vertices does a triangular pyramid have? Slide 22 (Answer) / 97 How many vertices does a triangular pyramid have? 10 Answer 4 [This object is a pull tab]
Slide 23 / 97 Volume Return to Table of Contents Slide 24 / 97 Volume 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 3 or cubic units click to reveal Slide 24 (Answer) / 97 Volume Volume MP.6: Attend to Precision. - The amount of space occupied by a 3-D Figure Math Practice click to reveal - The number of cubic units needed to FILL a 3-D Figure (layering) Ask: What labels (or units) should we use with our answers? Label - Units 3 or cubic units click to reveal [This object is a pull tab]
Slide 25 / 97 Volume Activity Click the link below for the activity. Lab #1: Volume Activity Slide 25 (Answer) / 97 Volume Activity Click the link below for the activity. Teacher Notes The URL for the lab is: http://njctl.org/courses/ math/8th-grade-math/3d- Lab #1: Volume Activity geometry/volume-activity/ [This object is a pull tab] Slide 26 / 97 Volume of Prisms & Cylinders Return to Table of Contents
Slide 27 / 97 Volume Volume of Prisms & Cylinders: Area of Base x Height, or V = Bh click to reveal Area Formulas: Rectangle = lw or bh click to reveal 1 Triangle = bh or (bh) click to reveal 2 2 Circle = πr 2 click to reveal Slide 28 / 97 Find the Volume 8 m 2 m 5 m Slide 28 (Answer) / 97 Find the Volume VOLUME: VOLUME: 2 V = B h Answer 8 m x 5 V = l w h 10 (Area of Base) V = 5 2 8 x 8 (Height) 2 m V = 10 8 80 m 3 5 m V = 80 m 3 [This object is a pull tab]
Slide 29 / 97 Find the Volume Use 3.14 as your value of π. 9 yd 10 yd Slide 29 (Answer) / 97 Find the Volume Use 3.14 as your value of π. 9 yd VOLUME: VOLUME: V = B h 9 Answer (Area of Base) x 9 V = r 2 h 10 yd 81 V = 3.14 9 2 10 x 3.14 V = 3.14 81 10 254.34 x 10 (Height) V = 254.34 10 2543.4 yd 3 V = 2543.4 yd 3 [This object is a pull tab] Slide 30 / 97 Find the Volume 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)(4) 2 (5) V = (3.14)(2) 2 (5) V = 251.2 cm 3 V = 62.8 cm 3 click click Answer the question. No, Amy is not correct. If the radius of the cylinder doubles, the volume does not double. Instead it quadruples. click
Slide 30 (Answer) / 97 Find the Volume A cylinder with a radius measuring 2 cm and a height of 5 MP.3 - Construct viable arguments & cm is compared to a cylinder with a radius of 4 cm and a critique the reasoning of others. 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 Math Practice After calculating the volume of both with a radius of 2 cm. She used 3.14 as her value of π. Is cylinders, ask: she correct? Explain your reasoning. What do you think about what Amy Start by calculating the volume of both cylinders. predicted? Do you agree? Why or Why not? V = (3.14)(4) 2 (5) V = (3.14)(2) 2 (5) V = 251.2 cm 3 V = 62.8 cm 3 click click [This object is a pull tab] Answer the question. No, Amy is not correct. If the radius of the cylinder doubles, the volume does not double. Instead it quadruples. click Slide 31 / 97 Teachers: Use this Mathematical Practice Pull Tab for the next 9 SMART Response slides. Slide 31 (Answer) / 97 Teachers: MP.5 - Use appropriate tools strategically. Use this Mathematical Practice Pull Tab for the next 9 Math Practice SMART Response slides. Ask: Can you make a model to show that? Would it help to create a diagram/draw a picture? [This object is a pull tab]
Slide 32 / 97 11 Find the Volume. 4 in 1 in 1 2 1 7 in 5 Slide 32 (Answer) / 97 11 Find the Volume. VOLUME: 7.2 x 1.5 4 in 10.8 (Area of Base) Answer x 4 (Height) 43.2 in 3 1 1 in VOLUME: 2 1 V = B h 7 in 5 V = 7.2(1.5)(4) V = 43.2 in 3 [This object is a pull tab] Slide 33 / 97 12 Find the volume of a rectangular prism with length 2 cm, width 3.3 cm and height 5.1 cm.
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