KS3 Mathematics S3 3-D shapes
S3 3-D shapes Contents S3.2 2-D representations of 3-D shapes S3.1 Solid shapes S3.3 Nets S3.4 Plans and elevations S3.5 Cross-sections
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? Face 12 How many vertices does a cube have? 8 Edge Vertex
Three-dimensional shapes Some examples of three-dimensional shapes include: A cube A cylinder A square-based pyramid A triangular prism A sphere A tetrahedron
Describing 3-D shapes made from cubes
Equivalent shape match
S3 3-D shapes Contents 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
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:
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.
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:
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?
Drawing 3-D shapes on an isometric grid
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.
Making shapes with four cubes You should have seven shapes altogether, as follows:
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.
Opposite faces Here are three views of the same cube. Each face is painted a different colour. What colours are opposite each other?
S3 3-D shapes Contents 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
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?
Nets
Nets What 3-D shape would this net make? A cuboid
Nets What 3-D shape would this net make? A triangular prism
Nets What 3-D shape would this net make? A tetrahedron
Nets What 3-D shape would this net make? A pentagonal prism
Nets of cubes Here is a net of a cube. M N A L B C K J D I H E G F When the net is folded up which sides will touch? A and B C and N D and M E and L F and I G and H J and K
Nets of cubes
Nets of dice
S3 3-D shapes Contents S3.1 Solid shapes S3.2 2-D representations of 3-D shapes S3.4 Plans and elevations S2.3 Nets S3.5 Cross-sections
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?
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:
Plans and elevations 2 cm Plan view 7 cm Side elevation Front elevation 3 cm 2 cm 3 cm 7 cm A solid can be drawn from various view points: 2 cm 3 cm 7 cm
Choose the shape Front elevation: Side elevation: Plan view: A: A: B: C:
Choose the shape Front elevation: Side elevation: Plan view: C: A: B: C:
Choose the shape Front elevation: Side elevation: Plan view: A: A: B: C:
Choose the shape Front elevation: Side elevation: Plan view: B: A: B: C:
Plans 2 2 1 1 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 represents this solid
Drawing shapes from plans
Shadows What solid shape could produce this shadow?
Shadows What solid shape could produce this shadow?
Shadows What solid shape could produce this shadow?
Shadows What solid shape could produce this shadow?
S3 3-D shapes Contents S3.1 Solid shapes S3.2 2-D representations of 3-D shapes S3.5 Cross-sections S3.3 Nets S3.4 Plans and elevations
Cross-sections Imagine slicing through a solid shape … … the 2-D shape produced is called a cross-section.
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,
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
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,
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,
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?
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.
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?
