Visualising solid shapes

Objectives

   1. Understanding the difference between 2D figures and 3D figures

   2. Identify views of 3D objects

   3. Make a connection between everyday objects and 3D shapes

   4. Students will be able to describe 3D shapes

   5. Verifying Euler’s formula for Polyhedrons.

Estimated Time

90 minutes

Prerequisites/Instructions, prior preparations, if any

Prior knowledge about 2D shapes and its properties

Materials/ Resources needed

Digital: Laptop, geogebra file, projector and a pointer.

Process (How to do the activity)

Download this geogebra file from this link.

  

• "What are some shapes that you know?"
•   Show picture of 2d and 3d and ask difference among shapes, What's the difference between 2D and 3D shapes?
•   Invite students to share the names of 2D and 3D shapes
•   What are 3 D shapes?
•   Visualizing solid shapes is a very useful skill. You should be able to see ‘hidden’parts of the solid shape.
•   Different sections of a solid can be viewed in many ways:

   (a) One way is to view by cutting or slicing the shape, which would result in the

      cross-section of the solid.

   (b)  Another way is by observing a 2-D shadow of a 3-D shape.

   (c) A third way is to look at the shape from different angles;

•       the front-view, the side-view and the top-view can provide a lot of information about the shape observed.
•       Rotate the object to find a top, side and bottom view of the solid.
•       Draw these views using pencil in your maths books, with a title "Top, side and bottom views of objects."

Download this geogebra file from this link.

• Do you remember the Faces, Vertices and Edges of solid shapes

• Students recall the terms edge, vertex, and face.

      Face - part of a 3D shape that is flat

      Edge-two faces meet at a line segment( A line where two faces meet in 3D shape)

      Vertex - three or more edges meet at a pointuk9caecz

      Base – the bottom base of a 3D shape

• Can you see that, the two-dimensional figures can be identified as the faces of the three-dimensional shapes?

Cuboid

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1. How many sides does a cuboid have ?
2. Are all sides the same ?
3. Point to its vertices. How many vertices does a cuboid have ?
4. Point to its edges and faces. How many are there ?
5. What is the shape of each of its face ? So how many squares and rectangles are there in a cuboid ?
6. Observe that shapes have two or more than two identical(congruent)faces?name them?
7. What are the properties of a cuboid ?  

Cube

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  # How many sides does a cube have ?

1. Are all sides the same ?
2. Point to its vertices. How many vertices does a cube have ?
3. Point to its edges and faces. How many are there ?
4. What is the shape of each of its face ? So how many squares are there in a cube ?
5. Which solids has all congruent faces?
6. What are the properties of a cube ?

Cylinder

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1. How many bases are in a cylinder?
2. What shape is the base of a cylinder?
3. How many edges does a cylinder have ?
4. How many vertices does a cylinder have ?
5. How many faces does a cylinder have ?
6. What are the properties of a cylinder?

Cone

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1. What shape is the base of a cone?
2. How many edges does a cone have ?
3. How many vertices does a cone have ?
4. How many faces does a cone have ?
5. What are the properties of a cone?

Sphere

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1. How many edges does a sphere have ?
2. How many vertices does a sphere have ?
3. How many faces does a sphere have ?
4. What are the properties of a sphere?  

• Does the base of the shape change depending on how the shape is positioned?
• Observe the shape of each face and find the number of faces of the box that are identical by placing them on each other. Write down your observations.

Cuboidal  box – all six faces are rectangular, and opposites faces are identical. So there are three pairs of identical faces.

Cubical box – All six faces are squares and identical

Cylindrical Box – One curved surface and two circular faces which are identical.

• A net is a sort of skeleton-outline in 2-D, which, when folded results in a 3-D shape.     

Euler’s formula for Polyhedrons (F+V=E+2)

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• What are polyhedrons?

Polyhedrons - Is a 3D solid which with flat polygonal faces, straight edges and sharp corners or vertices.

• Identify number of edges, faces and vertices in a given polyhedron ?

• Calculate F+V and E+2

• F+V = E+2 (Euler's Formula or Polyhedral formula)

• F+V-E=2

• The number of faces plus the number of vertices minus the number of edges equals 2.