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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
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.)
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
3-Dimensional Solids Return to Table of Contents
The following link will take you to a site with interactive 3-D figures and nets.
PolyhedronA 3-D figure whose faces are all polygons Polyhedron Not Polyhedron Sort the figures into the appropriate side.
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
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
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
Label each of the shapes as a pyramid or prism.
1Name the figure. ARectangular Prism B CHexagonal Prism DRectangular Pyramid ECylinder FCone Triangular Pyramid
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
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
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
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?
Volume of Prisms & Cylinders Return to Table of Contents
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
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!
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
18 What is the volume of the largest cylinder that can be placed into a cube that measures 10 feet on an edge?
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 .
Volume of Pyramids, Cones & Spheres Return to Table of Contents
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?
Demonstration comparing volume of Cones & Spheres with volume of Cylinders click to go to web site
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).
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).
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. $$$