KS3 Mathematics
S3 3-D shapes
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Contents
S3 3-D shapes
S3.1 Solid shapes
S3.2 2-D representations of 3-D shapes
S3.3 Nets
S3.4 Plans and elevations
S3.5 Cross-sections
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3-D shapes
3-D stands for three-dimensional.
3-D shapes have length, width and height.
For example, a cube has equal length, width and height.
How many faces does a
cube have? 6
How many edges does a
cube have? 12
Face
Edge
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Vertex
How many vertices does
a cube have? 8
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Three-dimensional shapes
Some examples of three-dimensional shapes include:
A cube
A triangular prism
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A square-based
pyramid
A sphere
A cylinder
A tetrahedron
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Describing 3-D shapes made from cubes
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Equivalent shape match
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Contents
S3 3-D shapes
S3.1 Solid shapes
S3.2 2-D representations of 3-D shapes
S3.3 Nets
S3.4 Plans and elevations
S3.5 Cross-sections
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2-D representations of 3-D shapes
When we draw a 3-D shape on a 2-D surface such as
a page in a book or on a board or screen, it is called a
2-D representation of a 3-D shape.
Imagine a shape made from four interlocking cubes
joined in an L-shape.
On a square grid we can draw the shape as follows:
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Drawing 3-D shapes on an isometric grid
The dots in an isometric grid form equilateral triangles
when joined together.
When drawing an 2-D representation of a 3-D shape
make sure that the grid is turned the right way round.
The dots should form clear vertical lines.
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Drawing 3-D shapes on an isometric grid
We can use an isometric grid to draw the four cubes joined
in an L-shape as follows:
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2-D representations of 3-D objects
There are several different ways of drawing the same shape.
Are these all of the possibilities?
Can you draw the shape in a different
way that is not shown here?
How many different ways are there?
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Drawing 3-D shapes on an isometric grid
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Making shapes with four cubes
How many different solids can you make with
four interlocking cubes?
Make as many shapes as you can from four cubes and
draw each of them on isometric paper.
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Making shapes with four cubes
You should have seven shapes altogether, as follows:
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Making shapes from five cubes
Investigate the number of different solids
can you make with five interlocking cubes.
Make as many as you can and draw each of them on
isometric paper.
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Opposite faces
Here are three views of the same cube.
Each face is painted a different colour.
What colours are opposite each other?
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Contents
S3 3-D shapes
S3.1 Solid shapes
S3.2 2-D representations of 3-D shapes
S3.3 Nets
S3.4 Plans and elevations
S3.5 Cross-sections
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Nets
Here is an example of a net:
This means that if you cut this shape out and folded it along
the dotted lines, you could stick the edges together to make
a 3-D shape.
Can you tell which 3-D shape it would make?
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Nets
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Nets
What 3-D shape would this net make?
A cuboid
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Nets
What 3-D shape would this net make?
A triangular prism
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Nets
What 3-D shape would this net make?
A tetrahedron
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Nets
What 3-D shape would this net make?
A pentagonal prism
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Nets of cubes
When the net is folded up
which sides will touch?
Here is a net of a cube.
M
N
A and B
A
L
B
C and N
C
D and M
K
J
D
I
H
E
G
F and I
G and H
F
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E and L
J and K
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Nets of cubes
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Nets of dice
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Contents
S3 3-D shapes
S3.1 Solid shapes
S3.2 2-D representations of 3-D shapes
S2.3 Nets
S3.4 Plans and elevations
S3.5 Cross-sections
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Shape sorter
A solid is made from cubes. By turning the shape it can
posted through each of these three holes:
Can you describe what this shape will look like?
Can you build this shape using interlocking cubes?
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Shape sorter
A solid is made from cubes. By turning the shape it can
posted through each of these three holes:
Here is a picture of the shape that will fit:
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Plans and elevations
A solid can be
drawn from various
view points:
Plan view
2 cm
7 cm
2 cm
3 cm
Front elevation
Side elevation
7 cm
3 cm
3 cm
2 cm
7 cm
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Choose the shape
Front elevation:
A:
A:
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Side elevation:
B:
Plan view:
C:
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Choose the shape
Front elevation:
A:
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Side elevation:
B:
Plan view:
C:
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Choose the shape
Front elevation:
A:
A:
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Side elevation:
B:
Plan view:
C:
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Choose the shape
Front elevation:
A:
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Side elevation:
B:
Plan view:
C:
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Plans
Sometimes the plan of a solid made from cubes has numbers
on each square to tell us the number of cubes are on that
base.
For example, this plan
2
2
1
1
represents this solid
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Drawing shapes from plans
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Shadows
What solid shape could produce this shadow?
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Shadows
What solid shape could produce this shadow?
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Shadows
What solid shape could produce this shadow?
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Shadows
What solid shape could produce this shadow?
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Contents
S3 3-D shapes
S3.1 Solid shapes
S3.2 2-D representations of 3-D shapes
S3.3 Nets
S3.4 Plans and elevations
S3.5 Cross-sections
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Cross-sections
Imagine slicing through a solid shape …
… the 2-D shape produced is called a cross-section.
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Cross-sections
Many different cross-sections can be produced by slicing
the same solid in different places.
For example, slicing a square-based pyramid can produce …
… squares,
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Cross-sections
Many different cross-sections can be produced by slicing
the same solid in different places.
For example, slicing a square-based pyramid can produce …
… triangles
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Cross-sections
Many different cross-sections can be produced by slicing
the same solid in different places.
For example, slicing a square-based pyramid can produce …
… trapeziums,
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Cross-sections
Many different cross-sections can be produced by slicing
the same solid in different places.
For example, slicing a square-based pyramid can produce …
… kites,
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Cross-sections
Many different cross-sections can be produced by slicing
the same solid in different places.
For example, slicing a square-based pyramid can produce …
… and pentagons.
Are any other
polygons possible?
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Cross-sections of prisms
A prism is a 3-D shape that has a constant cross-section
along its length.
For example, this hexagonal prism has the same hexagonal
cross-section throughout its length.
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Cross-sections of a square
A cube can be sliced to give a square cross-section.
Is it possible to slice a square to
produce a cross-section that is a
a) right-angled triangle
b) equilateral triangle
c) isosceles triangle
d) rectangle
e) rhombus
f) pentagon
g) hexagon?
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