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Images of 3-D

Learn about 3-dimensional figures, including solid geometric shapes and polygons. Understand their properties, such as faces, edges, and vertices. Discover examples and formulas to calculate the number of faces, edges, and vertices.

robertbperkins
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Images of 3-D

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  1. Images of 3-D

  2. What are 3-Dimentional Figures? Why do we need to learn about them?

  3. 3-Dimentional Figures • Solid Figures that are not on a flat plane. • 3-D Figures are seen in many ordinary objects around us. Let me show you some examples!

  4. Cones

  5. Cylinders

  6. Cubes

  7. Spheres

  8. Memphis Pyramid Egyptian Pyramid Pyramids

  9. Rectangular Prism

  10. What are Polygons? Define Closed 2-D figures formed by 3 or more line segments. Examples NOT Polygons Polygon Regular: All sides are equal Irregular: All sides are not equal

  11. Let’s Review Some Polygons Matching ____ Quadrilateral A. 3 sides ____ Octagon B. 4 sides ____ Decagon C. 5 sides ____ Hexagon D. 6 sides ____ Triangle E. 7 sides ____ Heptagon F. 8 sides ____ Pentagon G. 9 sides ____ Nonagon H. 10 sides

  12. Check Your Answers Matching B Quadrilateral A. 3 sides F Octagon B. 4 sides H Decagon C. 5 sides D Hexagon D. 6 sides A Triangle E. 7 sides E Heptagon F. 8 sides C Pentagon G. 9 sides G Nonagon H. 10 sides

  13. Moving on to 3-Dimentional Figures!

  14. Three-dimensional figures are not flat figures. They have length, width, and height. They are also called solid geometric figures. • The flat surfaces of three-dimensional figures are called faces. • The faces meet at edges. • The edges are line segments. • The edges meet at vertices (plural of vertex).

  15. Parts of a 3-D Figure Face – The flat surfaces. (Flat) Edge – Where the faces meet. (Straight Lines) Vertex – Where the edges meet. (Pointy Corners) Base - The top and bottom faces. 3-D Figure face vertex edge 6 faces 8 vertices 12 edges 2 faces no vertices no edges no faces no vertices no edges

  16. Examples of 3D Figures Prism Pyramid Cylinder Pentagonal Prism Triangular Prism Square Pyramid Triangular Pyramid Named by the shape of Also, named by the shape of Two bases that are circles. their two bases. its one base. Notice… the two bases have the The other faces are triangles. same shape! The other faces are rectangles. Cone Sphere Cube One vertex and a circular base. All points are the All faces are squares. same distance from a center point.

  17. 3-D Figures Solids! Prisms Pyramids Cylinders Cones Spheres Cubes Triangular prism Triangular Pyramid Rectangular Prism Square Pyramid Pentagonal Prism Pentagonal Pyramid Hexagonal Prism Hexagonal Pyramid

  18. Rectangular prism face base edge vertex A rectangular prism has 6 faces, 8 vertices, and 12 edges.

  19. face cube vertex edge A cube, just like a rectangular prism, has 6 faces (all squares), 8 vertices, and 12 edges.

  20. Triangular prism base base face face vertex A triangular prism has five faces. Its base is a triangle. (Notice that even when the triangular prism sits on a rectangle, the base is still a triangle.) Two of its faces are triangles; three of its faces are rectangles. It has six vertices and nine edges.

  21. Rectangular pyramid face vertex base A rectangular pyramid has 5 faces. Its base is a rectangle or a square and the other 4 faces are triangles. It has 8 edges and 5 vertices.

  22. vertex Triangular pyramid face base A triangular pyramid has four faces. All faces, including its base, are triangles. It has six edges and four vertices.

  23. Before We Move On Let’s Review • What are the flat surfaces of a 3D figure called? • Where do the faces meet? • What are the corners (or where the edges meet) called? • Which is the prism and which is the pyramid? A)B)

  24. How do I find the faces, edges, and vertices of a shape?

  25. Examples Pyramid Formula Formula Faces = # of sides of the base + # of the bases Vertices: # of faces Edges: faces+vertices-2 Faces: Edges: Vertices:

  26. Examples Prism Formula Formulas Use the following formulas to find the number of faces, edges, and vertices. Faces: # of sides of the base + # of bases Vertices: # of sides of the base x 2 Edges: Faces + Vertices - 2 Faces: Edges: Vertices:

  27. You Try! 1) 2) 3) Shape of Base: Shape of Base: Shape of Base: Name: Name: Name: 4) 5) 6) Shape of Base: Shape of Base: Shape of Base: Name: Name: Name: 7) 8) 9) Shape of Base: Shape of Base: Shape of Base: Name: Name: Name:

  28. You Try! – Check Your Answers 1) 2) 3) Shape of Base: Triangle Shape of Base: Circle Shape of Base: Hexagon Name: Triangular Prism Name: Cylinder Name: HexagonalPyramid 4) 5) 6) Shape of Base: Circle Shape of Base: None Shape of Base: Triangle Name: Cone Name: Sphere Name: Triangular Pyramid 7) 8) 9) Shape of Base: Square Shape of Base: Trapezoid Shape of Base: Square Name: Cube Name: Trapezoidal Prism Name: Square Pyramid

  29. You Try! 1) 2) 3) Faces: Vertices: Edges: Faces: Vertices: Edges: Faces: Vertices: Edges: 4) 5) 6) Faces: Vertices: Edges: Faces: Vertices: Edges: Faces: Vertices: Edges: 7) 8) 9) Faces: Vertices: Edges: Faces: Vertices: Edges: Faces: Vertices: Edges:

  30. You Try – Check Your Answers! 1) 2) 3) Faces: 5 Vertices: 6 Edges: 9 Faces: 2 Vertices: 0 Edges: 0 Faces: 7 Vertices: 7 Edges: 12 4) 5) 6) Faces: 1 Vertices: 1 Edges: 0 Faces: 0 Vertices: 0 Edges: 0 Faces: 4 Vertices: 4Edges: 6 7) 8) 9) Faces: 6 Vertices: 8 Edges: 12 Faces: 6 Vertices: 8 Edges: 12 Faces: 5 Vertices: 5Edges: 8

  31. Now it’s your turn! SHOWDOWN CAPTAIN!!!!

  32. Find the…. _____edges _____vertices _____faces

  33. Answer 16 edges 9 vertices 9 faces

  34. What shape am I? I am a solid figure that has a circular base. There are 2 faces in all. There is only 1 vertex There are no edges. What shape am I ?

  35. I am a….. Cone

  36. Find the…. _____edges _____vertices _____faces

  37. Answer 9 Edges 6 vertices 5 faces

  38. What is the name of a three-dimensional figure with six square faces? • pyramid • cube • solid • edge

  39. How many edges does a square pyramid have? • 4 • 5 • 7 • 8

  40. I am a three-dimensional figure with five faces. My base is a rectangle; my other faces are triangles. I have five vertices and eight edges. What am I? • rectangle prism • rectangular pyramid • triangular prism • triangular pyramid

  41. How many edges does a square pyramid have? • 4 • 5 • 7 • 8

  42. How many vertices does a rectangular prism have? • 12 • 8 • 6 • 4

  43. Which of the following has a base that is a triangle? • Triangular prism • Cube • Square pyramid • Rectangular pyramid

  44. I am a three-dimensional figure with four faces. All of my faces, including the base are triangles. What am I? • rectangular prism • triangular prism • triangular pyramid • rectangular pyramid

  45. How many faces of a cube are squares? • 2 • 4 • 6 • 8

  46. Sally is going to build a table for her family room. It is in the shape of a triangular prism. What shapes will she need to build the table? • 5 triangles • 2 triangles and 3 rectangles • 2 triangles and 4 rectangles • 6 rectangles

  47. Euler’s Formula We use Euler’s formula to check to see if all of our calculations are correct! Faces + Vertices – Edges= 2 If your numbers are correct, every time you plug them in it will equal 2!

  48. What in the World are Nets?

  49. What do you think of when someone mentions a net?

  50. Maybe you think of these?

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