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© Boardworks Ltd 2004 1 of 49 S3 3-D shapes KS3 Mathematics
© Boardworks Ltd 2004 2 of 49 Contents S3 3-D shapes A A A A A 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
© Boardworks Ltd 2004 3 of 49 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. Face EdgeVertex How many faces does a cube have? 6 How many edges does a cube have? 12 How many vertices does a cube have? 8
© Boardworks Ltd 2004 4 of 49 Three-dimensional shapes Some examples of three-dimensional shapes include: A triangular prism A square-based pyramid A cylinder A cube A sphereA tetrahedron
© Boardworks Ltd 2004 5 of 49 Describing 3-D shapes made from cubes
© Boardworks Ltd 2004 6 of 49 Equivalent shape match
© Boardworks Ltd 2004 7 of 49 Contents S3 3-D shapes A A A A A 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
© Boardworks Ltd 2004 8 of 49 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:
© Boardworks Ltd 2004 9 of 49 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.
© Boardworks Ltd 2004 10 of 49 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:
© Boardworks Ltd 2004 11 of 49 There are several different ways of drawing the same shape. Can you draw the shape in a different way that is not shown here? Are these all of the possibilities? How many different ways are there? 2-D representations of 3-D objects
© Boardworks Ltd 2004 12 of 49 Drawing 3-D shapes on an isometric grid
© Boardworks Ltd 2004 13 of 49 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
© Boardworks Ltd 2004 14 of 49 Making shapes with four cubes You should have seven shapes altogether, as follows:
© Boardworks Ltd 2004 15 of 49 Investigate the number of different solids you can make with five interlocking cubes. Make as many as you can and draw each of them on isometric paper. Making shapes from five cubes
© Boardworks Ltd 2004 16 of 49 Opposite faces Here are three views of the same cube. Each face is painted a different colour. What colours are opposite each other?
© Boardworks Ltd 2004 17 of 49 Contents S3 3-D shapes A A A A A S3.3 Nets S3.1 Solid shapes S3.2 2-D representations of 3-D shapes S3.4 Plans and elevations S3.5 Cross-sections
© Boardworks Ltd 2004 18 of 49 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?
© Boardworks Ltd 2004 19 of 49 Nets
© Boardworks Ltd 2004 20 of 49 Nets What 3-D shape would this net make? A cuboid
© Boardworks Ltd 2004 21 of 49 Nets What 3-D shape would this net make? A triangular prism
© Boardworks Ltd 2004 22 of 49 Nets What 3-D shape would this net make? A tetrahedron
© Boardworks Ltd 2004 23 of 49 Nets What 3-D shape would this net make? A pentagonal prism
© Boardworks Ltd 2004 24 of 49 Nets of cubes When the net is folded up which sides will touch? A andB C andN D andM E andL F andI G andH J andK Here is a net of a cube. MN A BC D E F G HI J K L
© Boardworks Ltd 2004 25 of 49 Nets of cubes
© Boardworks Ltd 2004 26 of 49 Nets of dice
© Boardworks Ltd 2004 27 of 49 Contents S3 3-D shapes A A A A A S3.4 Plans and elevations S3.1 Solid shapes S3.2 2-D representations of 3-D shapes S2.3 Nets S3.5 Cross-sections
© Boardworks Ltd 2004 28 of 49 Shape sorter A solid is made from cubes. By turning the shape it can be posted through each of these three holes: Can you describe what this shape will look like? Can you build this shape using interlocking cubes?
© Boardworks Ltd 2004 29 of 49 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:
© Boardworks Ltd 2004 30 of 49 Plans and elevations A solid can be drawn from various view points: 3 cm 7 cm 2 cm 7 cm Plan view 3 cm 7 cm Front elevation 3 cm 2 cm Side elevation
© Boardworks Ltd 2004 31 of 49 Front elevation:Side elevation:Plan view: Choose the shape A:B:C: A:
© Boardworks Ltd 2004 32 of 49 Front elevation:Side elevation:Plan view: Choose the shape A:B:C:
© Boardworks Ltd 2004 33 of 49 Front elevation:Side elevation:Plan view: Choose the shape A:B:C: A:
© Boardworks Ltd 2004 34 of 49 Choose the shape Front elevation:Side elevation:Plan view: A:B:C: B:
© Boardworks Ltd 2004 35 of 49 Plans Sometimes the plan of a solid made from cubes has numbers on each square to tell us the number of cubes on that base. For example, this plan: 221 1 represents this solid:
© Boardworks Ltd 2004 36 of 49 Drawing shapes from plans
© Boardworks Ltd 2004 37 of 49 Shadows What solid shape could produce this shadow?
© Boardworks Ltd 2004 38 of 49 Shadows What solid shape could produce this shadow?
© Boardworks Ltd 2004 39 of 49 Shadows What solid shape could produce this shadow?
© Boardworks Ltd 2004 40 of 49 Shadows What solid shape could produce this shadow?
© Boardworks Ltd of 49 S3 3-D shapes KS3 Mathematics.
© Boardworks Ltd of 49 Contents S3 3-D shapes A A A A A S3.1 Solid shapes S3.2 2-D representations of 3-D shapes S3.3 Nets S3.4 Plans and elevations.
© Boardworks Ltd of 84 This Chapter is going to show you How to estimate and calculate perimeters and areas of 2D shapes How to calculate the area.
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© Boardworks of 8 Nets. © Boardworks of 8 Here is an example of a net: If you cut this shape out and folded it along the dotted lines, you.
© Boardworks Ltd of 62 S10 Length, area and volume KS4 Mathematics.
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