KS3 Mathematics S3 3-D shapes 1 of 49 © Boardworks Ltd 2004
KS3 Mathematics S3 3-D shapes 1 of 49 © Boardworks Ltd 2004 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 2 of 49 © Boardworks Ltd 2004 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 3 of 49 Vertex How many vertices does a cube have? 8 © Boardworks Ltd 2004 Three-dimensional shapes Some examples of three-dimensional shapes include: A cube A triangular prism 4 of 49 A square-based pyramid A sphere A cylinder A tetrahedron © Boardworks Ltd 2004 Describing 3-D shapes made from cubes 5 of 49 © Boardworks Ltd 2004 Equivalent shape match 6 of 49 © Boardworks Ltd 2004 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 7 of 49 © Boardworks Ltd 2004 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: 8 of 49 © Boardworks Ltd 2004 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. 9 of 49 © Boardworks Ltd 2004 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: 10 of 49 © Boardworks Ltd 2004 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? 11 of 49 © Boardworks Ltd 2004 Drawing 3-D shapes on an isometric grid 12 of 49 © Boardworks Ltd 2004 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. 13 of 49 © Boardworks Ltd 2004 Making shapes with four cubes You should have seven shapes altogether, as follows: 14 of 49 © Boardworks Ltd 2004 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. 15 of 49 © Boardworks Ltd 2004 Opposite faces Here are three views of the same cube. Each face is painted a different colour. What colours are opposite each other? 16 of 49 © Boardworks Ltd 2004 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 17 of 49 © Boardworks Ltd 2004 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? 18 of 49 © Boardworks Ltd 2004 Nets 19 of 49 © Boardworks Ltd 2004 Nets What 3-D shape would this net make? A cuboid 20 of 49 © Boardworks Ltd 2004 Nets What 3-D shape would this net make? A triangular prism 21 of 49 © Boardworks Ltd 2004 Nets What 3-D shape would this net make? A tetrahedron 22 of 49 © Boardworks Ltd 2004 Nets What 3-D shape would this net make? A pentagonal prism 23 of 49 © Boardworks Ltd 2004 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 24 of 49 E and L J and K © Boardworks Ltd 2004 Nets of cubes 25 of 49 © Boardworks Ltd 2004 Nets of dice 26 of 49 © Boardworks Ltd 2004 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 27 of 49 © Boardworks Ltd 2004 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? 28 of 49 © Boardworks Ltd 2004 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: 29 of 49 © Boardworks Ltd 2004 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 30 of 49 © Boardworks Ltd 2004 Choose the shape Front elevation: A: A: 31 of 49 Side elevation: B: Plan view: C: © Boardworks Ltd 2004 Choose the shape Front elevation: A: 32 of 49 Side elevation: B: Plan view: C: © Boardworks Ltd 2004 Choose the shape Front elevation: A: A: 33 of 49 Side elevation: B: Plan view: C: © Boardworks Ltd 2004 Choose the shape Front elevation: A: 34 of 49 Side elevation: B: Plan view: C: © Boardworks Ltd 2004 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 35 of 49 © Boardworks Ltd 2004 Drawing shapes from plans 36 of 49 © Boardworks Ltd 2004 Shadows What solid shape could produce this shadow? 37 of 49 © Boardworks Ltd 2004 Shadows What solid shape could produce this shadow? 38 of 49 © Boardworks Ltd 2004 Shadows What solid shape could produce this shadow? 39 of 49 © Boardworks Ltd 2004 Shadows What solid shape could produce this shadow? 40 of 49 © Boardworks Ltd 2004 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 41 of 49 © Boardworks Ltd 2004 Cross-sections Imagine slicing through a solid shape … … the 2-D shape produced is called a cross-section. 42 of 49 © Boardworks Ltd 2004 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, 43 of 49 © Boardworks Ltd 2004 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 44 of 49 © Boardworks Ltd 2004 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, 45 of 49 © Boardworks Ltd 2004 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, 46 of 49 © Boardworks Ltd 2004 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? 47 of 49 © Boardworks Ltd 2004 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. 48 of 49 © Boardworks Ltd 2004 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? 49 of 49 © Boardworks Ltd 2004
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