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3D shapes

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visibility 56update a month agobookmarkshare

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.

Worked example

Imagine painting one face of these shapes.
Print that face onto paper.

Cube, cylinder and cuboid with example printed faces (square, circle, rectangle) to be matched

Match each print to the $3D$ shape that it comes from.

Answer:

The square print comes from the cube.

The circle print comes from the cylinder.

The rectangle print comes from the cuboid.

I think this comes from the cube because it has four straight sides.

I think this comes from the cylinder because it’s the only shape with no straight lines.

I think this comes from the cuboid because the $4$ sides are not the same length as each other.

EXERCISES

$1$. Fill in the missing numbers.

Question 1 table of 3D shapes (sphere, cuboid, cylinder, square-based pyramid, cube) with blanks for faces and vertices, plus a tip: curved surfaces do not count as faces

👀 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.

Question 3 sorting task with two circles for 'Has vertices' and 'Has no vertices', five shapes to sort, and two blank circles to sort again with 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.

Question 4 speech bubble game: 'I am a 3D shape with 6 square faces. What shape am I?' and answer bubble 'A cube.'

👀 Show answer

A cube.

$5$. Draw $3$ things that match these shapes. The first one is an example.

Question 5 table to draw three real objects for each shape: sphere (example globe), cylinder, cuboid, square-based pyramid, cube

👀 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?

Three different shapes made from four cubes (investigation diagrams)

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.

What we've learned

We learned to identify and name common $3D$ shapes such as a sphere, cylinder, cuboid, square-based pyramid, and cube.
We learned that a face is a flat surface, and curved surfaces do not count as faces.
We learned that a vertex is a corner, and shapes can have $0$, $5$, or $8$ vertices depending on their structure.
We practiced counting faces and vertices, including hidden faces in $3D$ drawings.
We sorted shapes by their properties, such as “has vertices” and “has no vertices”.
We connected $3D$ shapes to real-life objects and described how shapes can be built using $4$ cubes.

3D shapes

In this topic you will

Key Words

3D Shapes Around Us

Key Word: Vertex

EXERCISES

Think like a Mathematician

What we've learned

Related Past Papers

Related Tutorials

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