Contents

1. S3 3-D shapes • A Contents S3.2 2-D representations of 3-D shapes • A S3.3 Nets • A S3.1 Solid shapes S3.4 Plans and elevations • A S3.5 Cross-sections • A

2. 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

3. 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

4. S3 3-D shapes S3.1 Solid shapes • A Contents • A S3.3 Nets • A S3.2 2-D representations of 3-D shapes S3.4 Plans and elevations • A S3.5 Cross-sections • A

5. 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:

6. Opposite faces Here are three views of the same cube. Each face is painted a different colour. What colours are opposite each other?

7. S3 3-D shapes S3.1 Solid shapes • A Contents S3.2 2-D representations of 3-D shapes • A • A S3.3 Nets S3.4 Plans and elevations • A S3.5 Cross-sections • A

8. 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?

9. Nets

10. Nets What 3-D shape would this net make? A cuboid

11. Nets What 3-D shape would this net make? A triangular prism

12. Nets What 3-D shape would this net make? A tetrahedron

13. Nets What 3-D shape would this net make? A pentagonal prism

14. 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

15. Nets of cubes

16. Nets of dice

17. S3 3-D shapes S3.1 Solid shapes • A Contents S3.2 2-D representations of 3-D shapes • A S2.3 Nets • A S3.4 Plans and elevations • A S3.5 Cross-sections • A

18. 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

19. S3 3-D shapes S3.1 Solid shapes • A Contents S3.2 2-D representations of 3-D shapes • A S3.3 Nets • A S3.5 Cross-sections S3.4 Plans and elevations • A • A

20. Imagine slicing through a solid shape … Cross-sections … the 2-D shape produced is called a cross-section.

21. Many different cross-sections can be produced by slicing the same solid in different places. For example, slicing a square-based pyramid can produce … Cross-sections … squares,

22. Many different cross-sections can be produced by slicing the same solid in different places. For example, slicing a square-based pyramid can produce … Cross-sections … triangles

23. Many different cross-sections can be produced by slicing the same solid in different places. For example, slicing a square-based pyramid can produce … Cross-sections … trapeziums,

24. Many different cross-sections can be produced by slicing the same solid in different places. For example, slicing a square-based pyramid can produce … Cross-sections … kites,

25. Many different cross-sections can be produced by slicing the same solid in different places. For example, slicing a square-based pyramid can produce … Cross-sections … and pentagons. Are any other polygons possible?

26. 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 prisms

27. 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 Cross-sections of a square a) right-angled triangle b) equilateral triangle c) isosceles triangle d) rectangle e) rhombus f) pentagon g) hexagon?