Faces, Edges and Vertices of 3D Shapes
3D shapes (three-dimensional shapes) are solid objects that have length, width, and height. Unlike flat (2D) shapes, 3D shapes take up space.
In Class 3, you learn to describe 3D shapes by counting their faces, edges, and vertices. These three properties help you identify and compare different solid shapes.
Common 3D shapes include cubes, cuboids, cylinders, cones, spheres, and pyramids.
What is Faces, Edges and Vertices of 3D Shapes - Class 3 Maths (Geometry (Grade 3))?
Face: A flat surface of a 3D shape. Example: a cube has 6 faces.
Edge: The line where two faces meet. Example: a cube has 12 edges.
Vertex (plural: Vertices): A corner where edges meet. Example: a cube has 8 vertices.
Face = flat surface | Edge = line where faces meet | Vertex = corner point
Types and Properties
Common 3D Shapes and Their Properties
| Shape | Faces | Edges | Vertices |
|---|---|---|---|
| Cube | 6 | 12 | 8 |
| Cuboid | 6 | 12 | 8 |
| Cylinder | 3 (2 flat + 1 curved) | 2 | 0 |
| Cone | 2 (1 flat + 1 curved) | 1 | 1 |
| Sphere | 1 (curved) | 0 | 0 |
| Triangular Pyramid | 4 | 6 | 4 |
| Square Pyramid | 5 | 8 | 5 |
| Triangular Prism | 5 | 9 | 6 |
Note: Curved surfaces are sometimes counted as faces, but they are not flat faces. In Class 3, we count both flat and curved surfaces.
Solved Examples
Example 1: Example 1: Faces, Edges, Vertices of a Cube
Question: How many faces, edges, and vertices does a cube have?
Think:
- A cube is like a dice or a Rubik's cube
- Faces: 6 (all squares)
- Edges: 12 (where faces meet)
- Vertices: 8 (corners)
Answer: Cube: 6 faces, 12 edges, 8 vertices.
Example 2: Example 2: Cylinder
Question: How many flat faces does a cylinder have?
Think:
- A cylinder is like a tin can
- Top = 1 flat circle, Bottom = 1 flat circle
- Side = 1 curved surface (not flat)
Answer: A cylinder has 2 flat faces (and 1 curved surface).
Example 3: Example 3: Sphere
Question: How many edges and vertices does a sphere have?
Think:
- A sphere is like a ball
- It has no flat faces — only a curved surface
- No edges (no lines where flat faces meet)
- No vertices (no corners)
Answer: A sphere has 0 edges and 0 vertices.
Example 4: Example 4: Cone
Question: Describe the faces, edges, and vertices of a cone.
Think:
- A cone is like an ice cream cone
- 1 flat circular face (base)
- 1 curved surface
- 1 edge (the circular edge at the base)
- 1 vertex (the pointed tip at the top)
Answer: Cone: 1 flat face, 1 curved surface, 1 edge, 1 vertex.
Example 5: Example 5: Cuboid
Question: A book is in the shape of a cuboid. How many faces does it have?
Think:
- Front, back, top, bottom, left side, right side
- That is 6 faces (all rectangles)
Answer: A cuboid has 6 faces.
Example 6: Example 6: Identifying a Shape from Properties
Question: A 3D shape has 5 faces, 8 edges, and 5 vertices. What shape is it?
Think:
- Check the table: 5 faces, 8 edges, 5 vertices → Square Pyramid
Answer: It is a square pyramid.
Example 7: Example 7: Real-Life Objects
Question: Name a real-life object for each shape: cube, cylinder, cone.
Answer:
- Cube: Dice, sugar cube, Rubik's cube
- Cylinder: Water bottle, tin can, pipe
- Cone: Ice cream cone, traffic cone, party hat
Example 8: Example 8: Counting Edges of a Triangular Prism
Question: How many edges does a triangular prism have?
Think:
- A triangular prism has 2 triangular faces and 3 rectangular faces
- Each triangle has 3 edges = 6 edges (but 3 pairs are shared)
- Top triangle: 3 edges, bottom triangle: 3 edges, connecting edges: 3
- Total = 9 edges
Answer: A triangular prism has 9 edges.
Example 9: Example 9: Euler's Formula Check
Question: For a cube: Faces = 6, Vertices = 8, Edges = 12. Check if F + V − E = 2.
Think:
- F + V − E = 6 + 8 − 12 = 2 ✓
Answer: Yes, Euler's formula holds: F + V − E = 2.
Example 10: Example 10: Sorting Shapes
Question: Sort these into shapes with curved surfaces and shapes with only flat faces: cube, sphere, cylinder, cuboid, cone.
Think:
- Only flat faces: cube, cuboid
- Has curved surface: sphere, cylinder, cone
Answer:
Only flat faces: Cube, Cuboid
Has curved surface: Sphere, Cylinder, Cone
Real-World Applications
Where Do We See 3D Shapes?
- Buildings: Cuboid shapes for rooms, cylindrical pillars, dome (hemisphere) roofs.
- Packaging: Boxes (cuboid), cans (cylinder), Toblerone box (triangular prism).
- Sports: Football (sphere), cricket stumps (cylinder).
- Food: Ice cream cone (cone), dice sugar cubes (cube).
- Classroom: Globe (sphere), duster (cuboid), pencil (cylinder).
Key Points to Remember
- Face = flat surface of a 3D shape.
- Edge = line where two faces meet.
- Vertex = corner where edges meet.
- A cube has 6 faces, 12 edges, 8 vertices.
- A sphere has 0 edges and 0 vertices (only a curved surface).
- A cylinder has 2 flat faces, 1 curved surface, 2 edges, 0 vertices.
- Euler's formula: F + V − E = 2 (for shapes with only flat faces).
Practice Problems
- How many faces does a cuboid have? Are all faces the same?
- A shape has 1 vertex and 1 edge. What shape is it?
- Count the edges of a square pyramid.
- Name a 3D shape with no vertices.
- How many vertices does a triangular prism have?
- Name 3 real-life objects shaped like a cylinder.
- Check Euler's formula for a triangular pyramid: F=4, V=4, E=6. Does F+V−E=2?
Frequently Asked Questions
Q1. What is a face of a 3D shape?
A face is a flat surface on a 3D shape. For example, a cube has 6 flat square faces.
Q2. What is an edge?
An edge is the line where two faces of a 3D shape meet. A cube has 12 edges.
Q3. What is a vertex?
A vertex (plural: vertices) is a corner point where edges meet. A cube has 8 vertices.
Q4. Does a sphere have any faces?
A sphere has 1 curved surface but no flat faces. It also has no edges and no vertices.
Q5. What is the difference between a cube and a cuboid?
A cube has all faces as equal squares. A cuboid has rectangular faces — opposite faces are equal but not all faces are the same size.
Q6. What is Euler's formula?
Euler's formula states: Faces + Vertices − Edges = 2. It works for all polyhedra (3D shapes with only flat faces), like cubes, pyramids, and prisms.
Q7. How many faces does a cylinder have?
A cylinder has 3 surfaces: 2 flat circular faces (top and bottom) and 1 curved surface (the side).
Q8. Is a cone a 3D shape?
Yes. A cone is a 3D shape with 1 flat circular face, 1 curved surface, 1 edge, and 1 vertex (the tip).
Q9. How do I identify a 3D shape from its properties?
Count the faces, edges, and vertices. Compare with the known properties table. For example, 6 faces, 12 edges, 8 vertices = cube or cuboid.
