Investigating 3D Shapes and Nets Chapter Notes | Year 4 Mathematics IGCSE (Cambridge) - Class 4 PDF Download

The properties of 3D shapes

• The objective is to identify and describe the 2D faces of 3D shapes.
• Describe the properties of 3D shapes using appropriate vocabulary.
• Understanding 3D shape properties is essential for designing and constructing solid objects or containers, relevant to professions like artists, packaging designers, and architects.
• Key vocabulary for describing 3D shapes includes:
  • Face: A flat surface of a 3D shape, e.g., a square-based pyramid has 1 square face and 4 triangular faces.
  • Edge: A line segment where two faces meet.
  • Vertex: A point where two or more edges meet (plural: vertices).
• Common 3D shapes and their properties:
  • Square-based pyramid: Has 5 faces (1 square, 4 triangles).
  • Cuboid: Has 6 rectangular faces.
  • Triangular prism: Has 5 faces (2 triangles, 3 rectangles).
  • Pentagonal prism: Has 7 faces (2 pentagons, 5 rectangles).
  • Hexagonal pyramid: Has 7 faces (1 hexagon, 6 triangles).
  • Cone: Has 2 faces (1 circular base, 1 curved surface).
  • Cube: A special cuboid with 6 square faces.
• Describing shapes involves specifying the number and shape of faces, edges, and vertices to communicate properties clearly.

Nets of 3D shapes

• The objective is to match nets to the 3D shapes they form when folded.
• A net is a 2D shape that can be folded to create a 3D shape, representing the shape as if it were unfolded flat.
• Nets are practical in applications like cardboard packaging, where a net is drawn on card, cut out, and folded to form a box.
• Identifying a net involves:
  • Counting the number of faces in the net and ensuring it matches the 3D shape’s face count.
  • Verifying the shape of each face, e.g., a square-based pyramid’s net has 1 square and 4 triangles.
  • Ensuring the net folds without gaps or overlapping faces.
• Examples of nets and their corresponding 3D shapes:
  • Square-based pyramid: Net has 1 square and 4 triangles.
  • Tetrahedron (triangle-based pyramid): Net has 4 triangles, forming a shape with 4 faces.
  • Pentagonal prism: Net has 2 pentagons and 5 rectangles.
  • Octagon-based pyramid: Net has 1 octagon and 8 triangles.
  • Cone: Net has 1 circle and 1 curved sector.
  • Cylinder: Net has 2 circles and 1 curved rectangle.
• Patterns in pyramids and prisms:
  • Pyramids: The number of faces is n + 1, where nis the number of sides of the base, e.g.:
    • Triangle-based pyramid (tetrahedron): 3 + 1 = 4 faces.
    • Square-based pyramid: 4 + 1 = 5 faces.
    • Pentagon-based pyramid: 5 + 1 = 6 faces.
    • Hexagon-based pyramid: 6 + 1 = 7 faces.
    • Heptagon-based pyramid: 7 + 1 = 8 faces.
    • Nonagon-based pyramid: 9 + 1 = 10 faces.
    • Decagon-based pyramid: 10 + 1 = 11 faces.
  • Prisms: The number of faces is n + 2, where nis the number of sides of the base, e.g.:
    • Triangular prism: 3 + 2 = 5 faces.
    • Pentagonal prism: 5 + 2 = 7 faces.