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2. 7th Grade 3-D Geometry 2013-02-22 www.njctl.org

3. 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. • On the View tab, click Slide Master | Page Setup. Select On-screen Show (4:3) under Slide sized for and click Close Master View. • On the Slide Show menu, confirm that Resolution is set to 1024x768. • Use Slide Show View to Administer Assessment Items • To administer the numbered assessment items in this presentation, use the Slide Show view. (See Slide 11 for an example.)

4. Table of Contents Click on the topic to go to that section 3-Dimensional Solids Cross Sections of 3-Dimensional Figures Volume ·Prisms and Cylinders ·Pyramids, Cones & Spheres Surface Area ·Prisms ·Pyramids ·Cylinders ·Spheres More Practice/ Review Common Core: 7.G.3, 7.G.6, 7.EE.3

5. 3-Dimensional Solids Return to table of contents

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

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

8. 3-Dimensional Solids Categories & Characteristics of 3-D Solids: Prisms Have 2 congruent, polygon bases which are parallel to one another 2. Sides are rectangular (parallelograms) 3. Named by the shape of their base click to reveal 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

9. 3-Dimensional Solids Categories & Characteristics of 3-D Solids: Cylinders Have 2 congruent, circular bases which are parallel to one another 2. Sides are curved click to reveal Cones 1. Have 1 circular bases with a vertex opposite it 2. Sides are curved click to reveal

10. 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

11. Sort the figures. If you are incorrect, the figure will be sent back.

12. 1 Name the figure. A Rectangular Prism Triangular Pyramid B C Hexagonal Prism D Rectangular Pyramid E Cylinder F Cone

13. 2 Name the figure A Rectangular Pyramid B Triangular Prism C Octagonal Prism D Circular Pyramid E Cylinder F Cone

14. 3 Name the figure A Rectangular Pyramid B Triangular Pyramid C Triangular Prism D Hexagonal Pyramid E Cylinder F Cone

15. 4 Name the figure A Rectangular Prism B Triangular Prism C Square Prism D Rectangular Pyramid E Cylinder F Cone

16. 5 Name the figure A Rectangular Prism B Triangular Pyramid C Circular Prism D Circular Pyramid E Cylinder F Cone

17. 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?

18. 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

19. 6 How many faces does a pentagonal prism have?

20. 7 How many edges does a rectangular pyramid have?

21. 8 How many vertices does a triangular prism have?

22. Cross Sections of Three-Dimensional Figures Return to table of contents

23. 3-Dimensional figures can be cut by planes. When you cut a 3-D figure by a plane, the result is a 2-D figure. The cross-sections of 3-D figures are 2 dimensional figures you are familiar with. Look at the example on the next page to help your understanding.

24. A horizontal cross-section of a cone is a circle. Can you describe a vertical cross-section of a cone?

25. A vertical cross-section of a cone is a triangle.

26. A water tower is built in the shape of a cylinder. How does the horizontal cross-section compare to the vertical cross-section?

27. The horizontal cross-section is a circle. The vertical cross-section is a rectangle

28. 9 Which figure has the same horizontal and vertical cross-sections? A C B D

29. 10 Which figure does not have a triangle as one of its cross-sections? A C B D

30. 11 Which is the vertical cross-section of the figure shown? A Triangle B Circle C Square D Trapezoid

31. 12 Which is the horizontal cross-section of the figure shown? A Triangle B Circle C Square D Trapezoid

32. 13 Which is the vertical cross-section of the figure shown? A Triangle B Circle C Square D Trapezoid

33. Volume Return to table of contents

34. Volume 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 Units3 or cubic units click to reveal click to reveal

35. 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 if you add another layer and make it 4 x 2 x 3?

36. Volume of Prisms & Cylinders Return to table of contents

37. Volume Volume of Prisms & Cylinders: Area of Base x Height Area Formulas: Rectangle = lw or bh Triangle = bh or 2 Circle = r2 click to reveal click to reveal (bh) click to reveal click to reveal

38. Find the Volume. 8 m 2 m 5 m

39. Find the Volume. 9 yd 10 yd

40. 14 Find the Volume. 4 in 1 2 1 in 1 5 7 in

41. 15 Find the volume of a rectangular prism with length 2 cm, width 3.3 cm and height 5.1 cm.

42. 16 Which is a possible length, width and height for a rectangular prism whose volume = 18 cm3 A 1 x 2 x 18 B 6 x 3 x 3 C 2 x 3 x 3 D 3 x 3 x 3

43. 17 Find the volume.

44. 18 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? HINT: You may want to draw a picture!

45. 19 Find the volume. 10 m 6 m

46. 20 Which circular glass holds more water? A Glass A having a 7.5 cm diameter and standing 12 cm high B Glass B having a 4 cm radius and a height of 11.5 cm

47. 21 What is the volume of the largest cylinder that can be placed into a cube that measures 10 feet on an edge?

48. 22 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  .

49. Volume of Pyramids, Cones & Spheres Return to table of contents

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