3D shapes
In this topic you will
- Identify and describe 3D shapes around us.
- Sort and name 3D shapes.
Key Words
- curved surface
- edge
- face
- vertex
- vertices
Show Definitions
- curved surface: A surface that is not flat and bends smoothly, such as the outside of a sphere or cylinder.
- edge: A line where two faces of a 3D shape meet.
- face: A flat surface that forms part of a three-dimensional shape.
- vertex: A point where two or more edges meet in a three-dimensional shape.
- vertices: The plural of vertex; the corner points where edges meet in a 3D shape.
3D Shapes Around Us
You will see $3D$ shapes all around you but do you know what they are? This section will help you to recognise $3D$ shapes in different places. You will also learn more about spheres, cubes, cuboids, pyramids and cylinders.
Key Word: Vertex
A vertex is a corner. ‘Vertices’ is the plural of ‘vertex’ and means more than one corner.
EXERCISES
$1$. Fill in the missing numbers.
👀 Show answer
Sphere: It has $0$ faces and $0$ vertices.
Cuboid: It has $6$ faces and $8$ vertices.
Cylinder: It has $2$ faces and $0$ vertices.
Square-based pyramid: It has $5$ faces and $5$ vertices.
Cube: It has $6$ faces and $8$ vertices.
$2$. How many faces are hidden?
Cuboid: ________ faces are hidden
Cube: ________ faces are hidden
Square-based pyramid: ________ faces are hidden
Cylinder: ________ faces are hidden
👀 Show answer
Cuboid:$3$ faces are hidden.
Cube:$3$ faces are hidden.
Square-based pyramid:$2$ faces are hidden.
Cylinder:$1$ face is hidden.
$3$. Sort these shapes according to their properties.
Has vertices
Has no vertices
Sphere Cylinder Cuboid Pyramid Cube
Sort them in a different way.
Write your own labels.
👀 Show answer
Has vertices: Cuboid, Pyramid, Cube.
Has no vertices: Sphere, Cylinder.
One possible “different way”:
• Label Has a curved surface: Sphere, Cylinder.
• Label Only flat faces: Cuboid, Pyramid, Cube.
$4$. I am a $3D$ shape with $6$ square faces. What shape am I?
Play this game with a partner. Take turns to describe the faces of a $3D$ shape. Ask your partner to guess what it is.
👀 Show answer
A cube.
$5$. Draw $3$ things that match these shapes. The first one is an example.
👀 Show answer
Examples you could draw:
Sphere: globe (example), ball, orange.
Cylinder: tin can, candle, toilet roll.
Cuboid: book, brick, cereal box.
Square-based pyramid: pyramid model, pyramid tent, pyramid ornament.
Cube: dice, Rubik’s cube, ice cube.
Think like a Mathematician
Task: Make these shapes using $4$ cubes.
Instructions:
- Use $4$ cubes to build the shapes shown.
- Choose $1$ of the shapes.
- Write how you made it (describe the steps clearly so someone else could copy your shape).
- Read your instructions back to yourself and check they are clear.
- Try to imagine the shape from your instructions: could someone guess which shape you chose?
Write your method:
Step $1$: ________________________________________________
Step $2$: ________________________________________________
Step $3$: ________________________________________________
Step $4$: ________________________________________________
Step $5$: ________________________________________________
Challenge: Can someone guess which shape you chose from your instructions?
👀 show answer
Example set of instructions (for the “$3$ in a row + $1$ on top” shape):
- Place $3$ cubes in a straight row on the table.
- Put the $4$th cube on top of the middle cube in the row.
- Check the shape has $3$ cubes touching the table and $1$ cube stacked above.
How to check: Your instructions should mention where each cube goes (next to, on top of, or at the end) so the shape can be rebuilt without seeing the picture.