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This material is made freely available at www.njctl.org and is intended for the non-commercial use of students and teachers. These materials may not be used for any commercial purpose without the written permission of the owners. NJCTL maintains its website for the convenience of teachers who wish to make their work available to other teachers, participate in a virtual professional learning community, and/or provide access to course materials to parents, students and others. Click to go to website: www.njctl.org New Jersey Center for Teaching and Learning Progressive Mathematics Initiative

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8th Grade 3D Geometry www.njctl.org 2013-07-11

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Setting the PowerPoint View Use Normal View for the Interactive Elements To use the interactive elements in this presentation, do not select the Slide Show view. Instead, select Normal view and follow these steps to set the view as large as possible: On the View menu, select Normal. Close the Slides tab on the left. In the upper right corner next to the Help button, click the ^ to minimize the ribbon at the top of the screen. On the View menu, confirm that Ruler is deselected. On the View tab, click Fit to Window. Use Slide Show View to Administer Assessment Items To administer the numbered assessment items in this presentation, use the Slide Show view. (See Slide 12 for an example.)

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Table of Contents ·Prisms and Cylinders Volume ·Pyramids, Cones & Spheres Click on the topic to go to that section More Practice/ Review 3-Dimensional Solids Common Core Standards: 8.G.9

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3-Dimensional Solids Return to Table of Contents

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The following link will take you to a site with interactive 3-D figures and nets.

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PolyhedronA 3-D figure whose faces are all polygons Polyhedron Not Polyhedron Sort the figures into the appropriate side.

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3-Dimensional Solids Categories & Characteristics of 3-D Solids: Prisms 1. Have 2 congruent, polygon bases which are parallel to one another 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 3. Named by the shape of their base click to reveal

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3-Dimensional Solids Categories & Characteristics of 3-D Solids: Cylinders 1. Have 2 congruent, circular bases which are parallel to one another 2. Sides are curved Cones 1. Have 1 circular bases with a vertex opposite it 2. Sides are curved click to reveal

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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

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Label each of the shapes as a pyramid or prism.

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1Name the figure. ARectangular Prism B CHexagonal Prism DRectangular Pyramid ECylinder FCone Triangular Pyramid

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2Name the figure ARectangular Pyramid BTriangular Prism COctagonal Prism DCircular Pyramid ECylinder FCone

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3Name the figure ARectangular Pyramid BTriangular Pyramid CTriangular Prism DHexagonal Pyramid ECylinder FCone

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4Name the figure ARectangular Prism BTriangular Prism CSquare Prism DRectangular Pyramid ECylinder FCone

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5Name the figure ARectangular Prism BTriangular Pyramid CCircular Prism DCircular Pyramid ECylinder FCone

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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? NameFacesVerticesEdges Cube 6812 Rectangular Prism 6812 Triangular Prism 569 Triangular Pyramid 446 Square Pyramid 558 Pentagonal Pyramid 6610 Octagonal Prism 101624

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Euler's Formula F + V - 2 = E The number of edges is 2 less than the sum of the faces and vertices. click to reveal

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6How many faces does a pentagonal prism have?

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7How many edges does a rectangular pyramid have?

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8How many vertices does a triangular prism have?

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9How many faces does a hexagonal pyramid have?

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10How many vertices does a triangular pyramid have?

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Volume Return to Table of Contents

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Volume - The amount of space occupied by a 3-D Figure - The number of cubic units needed to FILL a 3-D Figure (layering) Label Units 3 or cubic units click to reveal

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Volume Activity Take unit cubes and create a rectangular prism with dimensions of 4 x 2 x 1. What happens to the volume if you add another layer and make it 4 x 2 x 2? What happens to the volume is you add another layer and make it 4 x 2 x 3?

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Volume of Prisms & Cylinders Return to Table of Contents

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Volume Volume of Prisms & Cylinders: Area of Base x Height Area Formulas: Rectangle = lw or bh Triangle = bh or 2 Circle = r 2 click to reveal (bh) click to reveal

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Find the Volume. 5 m 8 m 2 m

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Find the Volume. 10 yd 9 yd

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11Find the Volume. 7 in 1 5 1 in 1 2 4 in

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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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13Which is a possible length, width and height for a rectangular prism whose volume = 18 cm 3 A1 x 2 x 18 B6 x 3 x 3 C2 x 3 x 3 D3 x 3 x 3

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14Find the volume. 21 ft 42 ft 50 ft 47 ft

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15A 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? HINT: You may want to draw a picture!

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16Find the volume. 6 m 10 m

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17Which circular glass holds more water? AGlass A having a 7.5 cm diameter and standing 12 cm high BGlass B having a 4 cm radius and a height of 11.5 cm

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18 What is the volume of the largest cylinder that can be placed into a cube that measures 10 feet on an edge?

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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 for .

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Volume of Pyramids, Cones & Spheres Return to Table of Contents

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Given the same diameter and height for each figure, drag them to arrange in order of smallest to largest volume. How many filled cones do you think it would take to fill the cylinder? How many filled spheres do you think it would take to fill the cylinder?

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Demonstration comparing volume of Cones & Spheres with volume of Cylinders click to go to web site

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Volume of a Cone (Area of Base x Height) 3 (Area of Base x Height) 1 3 click to reveal A cone is 1/3 the volume of a cylinder with the same base area (B) and height (h).

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V = 2/3 (Volume of Cylinder) r 2 h ( ) 2/3 V= or V = 4/3 r 3 Volume of a Sphere click to reveal A sphere is 2/3 the volume of a cylinder with the same base area (B) and height (h).

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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? (Just Ice Cream within Cone. Not on Top) Volume and Mass used in portion control. $$$

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20Find the volume. 4 in 9 in

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21Find the Volume 5 cm 8 cm

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If the radius of a sphere is 5.5 cm, what is its volume?

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22 What is the volume of a sphere with a radius of 8 ft?

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23What is the volume of a sphere with a diameter of 4.25 in?

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Volume of a Pyramid (Area of Base x Height) 3 (Area of Base x Height) 1 3 1 3 click to reveal A pyramid is 1/3 the volume of a prism with the same base area (B) and height (h).

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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). V = Bh 1313 =5 m side length = 4 m V = Bh 1313

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24Find the Volume of a triangular pyramid with base edges of 8 in, base height of 4 in and a pyramid height of 10 in. 8 in 10 in 4 in

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25Find the volume. 8 cm 7 cm 15.3 cm

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More Practice / Review Return to Table of Contents

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26Find the volume. 15 mm 8 mm 22 mm

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27Find 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. HINT: Drawing a diagram will help!

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28 Find the volume of a square pyramid with base edge of 4 inches and pyramid height of 3 inches.

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29Find the Volume 9 m 12 m 11 m 6 m

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30Find the Volume 14 ft 21 ft

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31Find the Volume 8 in 6.9 in

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32Find the Volume 4 ft 7 ft 8 ft 9 ft

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33A cone 20 cm in diameter and 14 cm high was used to fill a cubical planter, 25 cm per edge, with soil. How many cones-ful of soil were needed to fill the planter? 20 cm 14 cm 25 cm

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34Find the Volume. 7 in 8 in 9 in 2 in

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Name a 3-D Figure that is not a polyhedron.

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Name a 3-D figure that has 6 rectangular faces.

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35Find the volume. 40 m 70 m 80 m

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