Visualising Solid Shapes
Focused last-minute revision with key concepts, formulas, worked examples, exam traps and practice.
Chapter Snapshot
- 3D solids have length, breadth and height/depth.
- Faces meet along edges and edges meet at vertices.
- A net is a flat pattern that folds into a solid.
- Different viewing directions give different 2D views.
- For many convex polyhedra, F + V - E = 2.
What You Will Learn
- Distinguish 2D and 3D shapes
- Count faces, edges and vertices
- Recognise nets of solids
- Interpret top, front and side views
- Apply Euler's formula to suitable polyhedra
Last-Minute Chapter Map
Use this chapter in three passes:
- Understand the core ideas.
- Memorise formulas and exam traps.
- Attempt the compact practice set without looking at the answers.
2D and 3D
A square is 2D; a cube is 3D. A solid occupies space. Polyhedra are solids with flat polygonal faces.
Faces, edges and vertices
A cube has 6 faces, 12 edges and 8 vertices. A cuboid has the same counts. A triangular prism has 5 faces, 9 edges and 6 vertices.
Nets
A net is a 2D arrangement of faces that can fold into a solid. Not every arrangement of six squares is a valid cube net.
Views
Top, front and side views are 2D projections of a 3D object from different directions. They are useful in technical drawing.
Euler relation
For many convex polyhedra, the number of faces plus vertices minus edges equals 2.
A 3D solid can be represented by nets and 2D views.
Formula Sheet
Formula / Key Relations
Euler's formula
Use for suitable polyhedra with flat faces.
Worked Examples
The formula is satisfied.
Exam Traps
Quick Revision
Quick Revision
- 3D solids have length, breadth and height/depth.
- Faces meet along edges and edges meet at vertices.
- A net is a flat pattern that folds into a solid.
- Different viewing directions give different 2D views.
- For many convex polyhedra, F + V - E = 2.
- Revise the formula sheet once more before attempting questions.
Compact Practice
Edges in a cube?
View Solution
12
Vertices in a cuboid?
View Solution
8
What is a net?
View Solution
A 2D pattern that folds into a 3D solid.
Why do top and front views differ?
View Solution
They are projections from different directions.
Final Chapter Summary
Chapter Summary
- 3D solids have length, breadth and height/depth.
- Faces meet along edges and edges meet at vertices.
- A net is a flat pattern that folds into a solid.
- Different viewing directions give different 2D views.
- For many convex polyhedra, F + V - E = 2.
- Prioritise correct method, clean working and final units where applicable.