The solid shown is a cube. How many faces does it have?
Faces are the flat surfaces.
A cube has 6 square faces.
3D Shapes and Nets
3D shapes have length, width and height, while nets show how solids unfold into flat shapes. This topic links closely to surface area, volume and perimeter and area, because understanding faces helps with later calculations.
Overview
A 3D shape is a solid object with length, width and height.
A net is a flat pattern that folds to make a 3D shape.
faces + edges + vertices = key shape properties
In exam questions, you are often asked to identify a shape, describe its properties, or decide whether a net can fold into the correct solid.
What you should understand after this topic
- Recognise common 3D shapes
- Understand faces, edges and vertices
- Relate nets to 3D solids
- Decide if a net will fold correctly
- Use shape properties in exam questions
Key Definitions
3D Shape
A solid shape with three dimensions: length, width and height.
Face
A flat or curved surface on a 3D shape.
Edge
The line where two faces meet.
Vertex
A corner where edges meet. The plural is vertices.
Net
A 2D pattern that folds to make a 3D shape.
Cross Section
The shape made when a 3D object is cut straight through.
Key Rules
Count carefully
Faces, edges and vertices must all match the shape.
Curved surfaces are not flat faces
A cylinder and cone include curved surfaces.
A net must fold without overlap
If faces clash or leave gaps, it is not a valid net.
Base shape matters
The base often tells you the name of the prism or pyramid.
Quick Property Guide
Cube
All faces are equal squares.
Cuboid
All faces are rectangles, not necessarily equal.
Prism
Same cross section all the way through.
Pyramid
Faces meet at one top vertex.
How to Solve
Step 1: Identify the solid shape
Start by looking at the faces, edges and vertices. Ask whether the shape has square, rectangular, triangular or circular faces, and check whether it has any curved surfaces.
If all 6 faces are squares, the shape is a cube.
If all faces are rectangles, the shape is a cuboid.
If there are 2 circles and one curved surface, the shape is a cylinder.
Exam tip: Always identify the shape before attempting any calculation or drawing.
Step 2: Count faces, edges and vertices
Counting faces, edges and vertices is often the quickest way to confirm the shape.
Why this matters: Different shapes can look similar, but their properties confirm the correct answer.
Cube
6 faces, 12 edges, 8 vertices
Cuboid
6 faces, 12 edges, 8 vertices
Cylinder
2 flat circular faces, 1 curved surface, 2 circular edges, 0 vertices
Triangular prism
5 faces, 9 edges, 6 vertices
Step 3: Understand what a net shows
A net is the flat version of a 3D shape before it is folded. Each face in the net becomes a face on the final solid.
A cube net is made from 6 equal squares.
A cuboid net is made from 6 rectangular faces.
A cylinder net includes 2 circles and 1 rectangle.
Nets are especially useful when finding surface area, because surface area means adding the areas of all faces.
Exam tip: Imagine folding the net in your mind to check whether the faces meet correctly.
Step 4: Check whether the net works
A correct net must:
Why this matters: Many exam questions include invalid nets designed to test careful checking.
- have the right number of faces
- have the correct shapes of faces
- fold without overlapping
- close fully with no missing face
Step 5: Link nets to later calculations
Once you understand the faces of a 3D shape, it becomes easier to calculate measurements.
For the calculation side, continue with surface area and volume.
Surface area
Add the area of every face in the net.
Volume
Find the space inside the solid.
Perimeter and area
Use 2D face calculations before moving to 3D calculations.
Example Questions
Edexcel
Exam-style questions focusing on recognising 3D shapes and counting their properties.
Edexcel
The solid shown is a cube.
How many faces does a cube have?
Edexcel
The solid shown is a cuboid.
How many vertices does a cuboid have?
AQA
Exam-style questions focusing on cylinders, cones and matching 3D shapes to their properties.
AQA
The 3D shape shown has 2 circular faces and 1 curved surface.
Name the 3D shape.
AQA
The 3D shape shown has one circular base and one vertex.
Explain why this shape is a cone.
OCR
Exam-style questions focusing on nets and whether a net folds correctly.
OCR
A net is made from 6 equal squares.
Which solid does this net form?
OCR
This net has the correct number of square faces, but it may not fold into a cube.
Why might a net with the correct faces still be wrong?
OCR
A net contains two circles and one rectangle.
Which 3D shape does this net form?
Exam Checklist
Step 1
Look at the type of faces first.
Step 2
Count faces, edges and vertices carefully.
Step 3
For nets, check the number and shape of the faces.
Step 4
Imagine folding the net to see if it overlaps or leaves a gap.
Most common exam mistakes
Mixing up edges and vertices
Edges are lines, vertices are corners.
Ignoring curved surfaces
Shapes like cones, cylinders and spheres include curved parts.
Assuming every square net works
Not every arrangement folds into a cube.
Not visualising the fold
A valid net must close properly with no overlap.
Common Mistakes
These are common mistakes students make when working with 3D shapes and nets in GCSE Maths.
Confusing edges and vertices
Incorrect
A student says a cube has 8 edges.
Correct
A cube has 12 edges and 8 vertices. Edges are the line segments where faces meet, while vertices are the corner points.
Not distinguishing curved and flat surfaces
Incorrect
A student counts the curved surface of a cylinder as a face.
Correct
Curved surfaces are not flat faces. A cylinder has 2 flat circular faces and 1 curved surface.
Assuming any layout forms a cube net
Incorrect
A student thinks any arrangement of 6 squares can fold into a cube.
Correct
Only specific arrangements of 6 squares form a valid cube net. Some layouts overlap or leave gaps when folded.
Ignoring overlap when folding nets
Incorrect
A net is accepted even though two faces overlap when folded.
Correct
A valid net must fold without any faces overlapping. Always visualise or test how the shape folds.
Mixing up cube and cuboid properties
Incorrect
A student says all cuboids have equal edges like a cube.
Correct
A cube is a special type of cuboid where all edges are equal. In a general cuboid, edge lengths can be different.
Try It Yourself
Test yourself on shape names, properties and nets.
Foundation
Foundation Practice
Recognise common 3D shapes, count faces, edges and vertices, and match simple nets.
The solid shown is a cuboid. How many vertices does it have?
Vertices are corners.
A cuboid has 8 vertices.
Name the 3D shape shown.
It has two circular faces.
The shape is a cylinder.
The shape shown has one circular base and one vertex. Name the shape.
Think of an ice cream cone.
The shape is a cone.
Which statement describes a sphere?
A sphere is completely curved.
A sphere has one curved surface and no edges or vertices.
How many edges does a cube have?
Edges are where two faces meet.
A cube has 12 edges.
The net shown is made from 6 equal squares. Which solid does it form?
A cube has 6 square faces.
This net forms a cube.
The triangular prism shown has 2 triangular faces and 3 rectangular faces. How many faces does it have altogether?
Add 2 triangular faces and 3 rectangular faces.
2 + 3 = 5 faces.
The solid shown is a square-based pyramid. How many vertices does it have?
There are 4 base corners and 1 top corner.
A square-based pyramid has 5 vertices.
A net contains two circles and one rectangle. Which 3D shape does it form?
The rectangle wraps around to make the curved surface.
This is the net of a cylinder.
Higher
Higher Practice
Reason about nets, hidden faces, Euler’s formula and properties of prisms and pyramids.
A prism has a pentagonal cross-section. How many faces does it have?
It has 2 pentagons and 5 rectangular faces.
2 pentagonal faces + 5 rectangular faces = 7 faces.
A pentagonal prism has 10 vertices and 7 faces. Use Euler’s formula to find the number of edges.
Substitute into F + V − E = 2.
7 + 10 − E = 2, so E = 15.
Which net forms a cylinder?
A cylinder has two circular ends.
A cylinder net has 2 circles and 1 rectangle.
The prism shown has a hexagonal cross-section. How many faces does a hexagonal prism have?
It has 2 hexagons and 6 rectangular faces.
2 + 6 = 8 faces.
A square-based pyramid has 5 faces and 5 vertices. How many edges does it have?
Use F + V − E = 2.
5 + 5 − E = 2, so E = 8.
A triangular prism has 5 faces and 6 vertices. Use Euler’s formula to find the number of edges.
Substitute 5 and 6 into Euler’s formula.
5 + 6 − E = 2, so E = 9.
This arrangement has 6 square faces. Why might it still fail to make a cube?
Correct number of faces is not enough.
A net must fold without overlap to make the solid.
A cuboid has 6 faces and 8 vertices. Use Euler’s formula to find the number of edges.
Use F + V − E = 2.
6 + 8 − E = 2, so E = 12.
Which statement is true for all prisms?
Think about slicing through the shape.
A prism has the same cross-section all the way through.
A prism has an octagonal cross-section. How many faces does it have?
For an n-sided prism, faces = n + 2.
2 octagonal faces + 8 rectangular faces = 10 faces.
Games
Practise this topic with interactive games.
Games coming soon.
Frequently Asked Questions
What is a net?
A flat shape that folds into a 3D object.
What is a vertex?
A point where edges meet.
Why are nets important?
They help calculate surface area.