3D shapes
🎯 In this topic you will
- Explore a range of 3D shapes and recognise their key features.
- Identify, describe, and sort different 3D shapes.
- Compare 3D shapes by explaining what is the same and what is different.
- Identify the faces and edges of common 3D shapes.
- Use the correct mathematical vocabulary when talking about 3D shapes.
🧠 Key Words
- 3D
- cube
- cylinder
- edge
- face
- sphere
- cuboid
- pyramid
Show Definitions
- 3D: Describes objects that have three dimensions: length, width, and height.
- cube: A 3D shape with six equal square faces, twelve edges, and eight vertices.
- cylinder: A 3D shape with two parallel circular faces connected by one curved surface.
- edge: A line where two faces of a 3D shape meet.
- face: A flat or curved surface that forms part of the boundary of a 3D shape.
- sphere: A perfectly round 3D shape with no edges or vertices, where every point on the surface is the same distance from the centre.
- cuboid: A 3D shape with six rectangular faces, where opposite faces are equal.
- pyramid: A 3D shape with a polygon base and triangular faces that meet at a single point.
🏡 3D Shapes in Everyday Life
We live inside 3D shapes.
We have 3D shapes all around us
and you can even hold a 3D shape in your hand.
🔍 Faces and Edges of 3D Shapes
3D shapes have faces. Many also have edges.
🟠 Flat Faces and Curved Surfaces
3D shapes can have flat faces or curved surfaces.
❓ EXERCISES
1. Look at the pictures of $3$D shapes. Join the shapes that are the same.
👀 Show answer
2.
a. Draw a ring around the cubes.
b. Colour the cylinders yellow.
c. Colour the spheres blue.
👀 Show answer
b. The cylinders are the solids with two circular faces and one curved surface — colour them yellow.
c. The spheres are the round ball shapes — colour them blue.
3.
a. Draw a ring around the shapes that will roll.
b. Draw a ring around the shapes that you can stack.
👀 Show answer
b. Shapes that stack: cube (because it has flat faces).
4. Look at the shapes in question $3$. Which $3$D shapes fit onto these $2$D shapes? Which $3$D shape is missing?
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5. Join the name of the shape to the shape itself. The first one has been done for you.
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sphere → round ball shape
cylinder → can-shaped solid
6. How many edges and faces does each shape have?
👀 Show answer
Sphere: $0$ edges, $0$ faces (one curved surface).
Cylinder: $2$ edges, $2$ flat faces and $1$ curved surface.
🧠 Think like a Mathematician
Build a tower using different $3$D shapes. You can use more than one of each shape. Talk about your tower and the shapes you will use. Use the words edge and face.
Follow-up Questions:
Show Answers
- 1: A cube (or cuboid) is best to start with because it has flat faces that make a stable base.
- 2: A sphere or cylinder is better at the top because curved shapes are less stable and work better when placed higher rather than at the base.
📦 What Is a 3D Shape?
A 3D shape takes up space.
🟦 Properties of a Cube
A cube is a 3D shape with 6 faces. Each face is a square. All the edges of a cube are the same length.
🔺 Understanding Pyramids
The base of a pyramid can be any straight-sided shape, such as a square or a triangle. The other faces are triangles that meet at the top. The number of faces depends on the shape of the base.
🥫 Features of a Cylinder
Cylinders have two flat ends that are both the same size and are circles. The flat ends are joined by a surface that is curved, not flat.
📘 All About Cuboids
A cuboid is a 3D shape with 6 flat faces. All of its faces are rectangles. There are lots of other 3D shapes for you to explore.
❓ EXERCISES
1. Work with a partner. Look at these pairs of shapes. What is the same and what is different?
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2. Misha has made a pattern with some shapes.
Make your own pattern with shapes.
Tell your partner about your pattern. Can they make it longer?
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3. Name the shapes of the faces that are coloured.
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Cube: square.
Pyramid: triangle.
4.
How many faces does the cube have?
How many edges does the cube have?
How many faces does the cuboid have?
How many edges does the cuboid have?
👀 Show answer
Cuboid: $6$ faces and $12$ edges.
🧠 Think like a Mathematician
Pick a shape and hold it in your hand.
Look at one face of the shape and name the shape of the face you see.
Turn the shape.
Say “same” when you see a face with the same shape.
Try with different shapes. What do you notice?
Follow-up Questions:
Show Answers
- 1: Some shapes have faces that are all the same (like a cube with square faces). Other shapes have faces that are different or include curved surfaces (like a cylinder or pyramid). Turning the shape helps you see whether the faces match.
❓ EXERCISES
5. Salif has $2$ different pyramids. Draw the shapes that could be the bases.
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6. What is the same and what is different about a sphere and a cylinder?
Draw a ring round the model that would fall over if you built it on a table.
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Different: A cylinder has $2$ flat circular faces and edges; a sphere has no flat faces and no edges.
The model that would fall over is the one balanced on the sphere (right-hand model).
7. Look at these shapes.
Choose four of them to build a tower.
Show your tower to your teacher.
👀 Show answer
8. What shape am I?
I have $6$ flat faces.
All my faces are square. ____________________
I have $5$ flat faces.
$1$ face is a square and $4$ faces are triangles. ____________________
I have $2$ flat faces and $1$ curved surface.
My flat faces are circles. ____________________
Choose a $3$D shape and write a set of clues for it.
👀 Show answer
$5$ faces (square base and $4$ triangles) → square-based pyramid.
$2$ flat circular faces and $1$ curved surface → cylinder.
Final task: answers will vary depending on the clues written.
🧠 Think like a Mathematician
You need $5$ cubes of the same size.
Pick up one cube. Count how many faces it has. Write your answer in the table.
Table to complete:
| Number of cubes in the shape | Number of faces |
|---|---|
| $1$ | |
| $2$ | |
| $3$ | |
| $4$ | |
| $5$ |
Now put two cubes together. Count how many faces the new shape has. Is there a different number of faces?
Keep adding cubes and counting the number of faces. Write your findings in the table.
What happens to the number of faces when you add more cubes?
Follow-up Questions:
Show Answers
- 1: One cube has $6$ faces.
- 2: The number of outer faces increases, but not by $6$ each time. When cubes join, some faces become hidden.
- 3: When two cubes touch, the touching faces are no longer on the outside, so they are not counted. This is why the total increases more slowly.