Images of 3 D What are 3 Dimentional

Images of 3 -D

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

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!

Cones

Cylinders

Cubes

Spheres

Memphis Pyramid Egyptian Pyramids

Rectangular Prism

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

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

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

Moving on to 3 -Dimentional Figures!

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).

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) 3 -D Figure Base - The top and bottom faces. face vertex edge 6 faces 8 vertices 12 edges 2 faces no vertices no edges no faces no vertices no edges

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

3 -D Figures Prisms Triangular prism Rectangular Prism Pentagonal Prism Hexagonal Prism Pyramids Triangular Pyramid Square Pyramid Pentagonal Pyramid Hexagonal Pyramid Cylinders Cones So lid Spheres Cubes s!

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

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

Triangular prism base 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.

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.

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

Before We Move On Let’s Review What are the flat surfaces of a 3 D 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)

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

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

Prism Formulas Examples 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:

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

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

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

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

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

Find the…. _____edges _____vertices _____faces

Answer 16 edges 9 vertices 9 faces

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 ?

I am a…. . Cone

Find the…. _____edges _____vertices _____faces

Answer 9 Edges 6 vertices 5 faces

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

How many edges does a square pyramid have? a. b. c. d. 4 5 7 8

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? a. b. c. d. rectangle prism rectangular pyramid triangular prism triangular pyramid

How many edges does a square pyramid have? a. b. c. d. 4 5 7 8

How many vertices does a rectangular prism have? a. b. c. d. 12 8 6 4

Which of the following has a base that is a triangle? a. b. c. d. Triangular prism Cube Square pyramid Rectangular pyramid

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

How many faces of a cube are squares? a. b. c. d. 2 4 6 8

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? a. b. c. d. 5 triangles 2 triangles and 3 rectangles 2 triangles and 4 rectangles 6 rectangles

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!

What in the World are Nets?

What do you think of when someone mentions a net?

Maybe you think of these?

Orange Roughy anyone? (New Zealand) Cold water coral reef.

Let’s talk about, NETS in MATH! ! ! Definition: A Net is a 2 -dimensional pattern that you can fold to form a 3 -dimensional figure. Example: Figure 1 Figure 2

Challenge: Which of the nets can be folded to form a cube? Hint: Think about how many faces a cube has!

A net is a 2 -D pattern like A 2 -D sewing pattern That forms a 3 -D solid shape Forms a 3 -D outfit

Let’s learn a little more about a 3 -D net. http: //www. virtualnerd. com/geometry/surface-areavolume-solid/introduction/three-dimensional-figurefrom-net

Let’s practice identifying a 3 -D figure from a net. Prism or Pyramid?

Identify the 3 -D figure from the net. Prism or Pyramid?

Identify the 3 -D figure from the net. Prism or Pyramid?

Identify the 3 -D figure from the net.

Identify the 3 -D figure from the net.

Identify the 3 -D figure from the net.

Identify the 3 -D figure from the net. Match the letter to the number. A. ____ B. ____ C. ____ D. ____ E. ____ F. ____ G. ____