Learning Objectives
- Identify 3D shapes: cubes, cuboids, cylinders, cones, spheres, pyramids, prisms
- Understand faces, edges, and vertices of solid shapes
- Draw nets of 3D shapes
- Visualise cross-sections and shadows of solids
Key Concepts
Faces, Edges, and Vertices
Every solid shape has:
- Faces: Flat surfaces of the solid
- Edges: Line segments where two faces meet
- Vertices: Points where edges meet
Euler's Formula
F + V - E = 2
Where F = Faces, V = Vertices, E = Edges
This holds for all convex polyhedra.
Common 3D Shapes
- Cube: 6 faces, 12 edges, 8 vertices
- Cuboid: 6 faces, 12 edges, 8 vertices
- Triangular Prism: 5 faces, 9 edges, 6 vertices
- Square Pyramid: 5 faces, 8 edges, 5 vertices
- Cylinder: 3 faces (2 flat + 1 curved), 2 edges, 0 vertices
- Cone: 2 faces (1 flat + 1 curved), 1 edge, 1 vertex
- Sphere: 1 curved face, 0 edges, 0 vertices
Nets of Solids
A net is a flat pattern that can be folded to form a 3D shape. Different solids have different nets.
Summary
Solid shapes are three-dimensional objects with length, breadth, and height. They are characterised by their faces, edges, and vertices. Euler's formula (F + V - E = 2) relates these for polyhedra. Nets help understand how 3D shapes are constructed from flat surfaces.
Important Terms
- Polyhedron
- A 3D shape with flat polygonal faces (e.g., cube, pyramid)
- Prism
- A polyhedron with two identical parallel bases connected by rectangular faces
- Pyramid
- A polyhedron with a polygonal base and triangular lateral faces meeting at a point
- Net
- A 2D pattern that folds into a 3D shape
Quick Revision
- Euler's formula: F + V - E = 2
- A cube has 6 faces, 12 edges, 8 vertices
- Cylinder has 2 flat faces and 1 curved surface
- Cone has 1 flat face, 1 curved surface, and 1 vertex (apex)
- A sphere has only 1 curved surface, no edges or vertices
Practice Tips
- Count faces, edges, and vertices of objects around you
- Verify Euler's formula for different shapes
- Draw and cut out nets of cubes and pyramids, then fold them