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3D Solids

3D Solids. Can you name the 3D solids with below?. Square-based pyramid. Cube. Cuboid. Sphere. Cylinder. Cone. The buildings are cuboids. The street lights are spheres. The chimneys are cylinders. One roof is a square-based pyramid. What mathematical solids can you see?. B. M. G.

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3D Solids

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  1. 3D Solids • Can you name the 3D solids with below? • Square-based pyramid • Cube • Cuboid • Sphere • Cylinder • Cone

  2. The buildings are cuboids • The street lights are spheres • The chimneys are cylinders • One roof is a square-based pyramid • What mathematical solids can you see?

  3. B • M • G • A • K • K • H • H • C • N • F • D • I • J • L • E • E Starter Which of the following shapes are: • Polygons? • Prisms? • Polyhedra? • None of these? •  A 2D shape with only straight sides •  A 3D shape with a consistent cross-section (Some prisms are also polyhedra!) •  A 3D shape with flat faces and straight edges

  4. Prisms • Circular prism or cylinder • Rectangular prism or cuboid A prism is a solid which has the same cross-section along its length. • Trapezoidal prism • Triangular prism

  5. Which of these solids is a prism?

  6. Faces, Edges and Vertices

  7. Faces, Edges and Vertices Face:  The faces of a shape are its ‘sides’. They are areas • VERTEX • EDGE • VERTEX • FACE • EDGE • EDGE • EDGE • VERTEX • VERTEX Edge:  The edges of a shape are the lines that make it’s ‘skeleton’ • EDGE • FACE • FACE • EDGE • EDGE • VERTEX • EDGE • EDGE Vertex/Vertices:  The vertices of a shape are its ‘corners’ • VERTEX • VERTEX

  8. Faces, Edges and Vertices • So how many Faces, Edges and Vertices does this cube have? • Faces: • Edges: • Vertices: • 6 • 12 • 8

  9. Faces, Edges and Vertices • So how many Faces, Edges and Vertices does this Square-based Pyramid have? • Faces: • Edges: • Vertices: • 5 • 8 • 5

  10. Faces, Edges and Vertices • Complete the following table: Shape Sketch Faces Edges Vertices Cube 6 12 8 Cuboid 6 12 8 Tetrahedron 4 6 4 Square-based Pyramid 5 8 5 Pentagonal-based Pyramid 6 10 6 Triangular Prism 5 9 6 Hexagonal Prism 8 18 12 Cylinder 3 2 0 Cone 2 1 1 Sphere 1 0 0 Frustum 6 12 8

  11. Plenary • What is the link between Faces , Edges and Vertices in the Polyhedra? • Cube • Square-based Pyramid • Hexagonal Prism

  12. Plenary • or This formula was discovered by Leonhard Euler, a Swiss mathematician considered to be one of the most prolific of all time… Knowing this formula allowed mathematicians to further investigate the properties of 3D objects. You can also set people impossible ‘trick’ tasks! • Leonhard Euler (1707-1783) “Draw a polyhedron with 5 faces, 8 vertices and 10 edges” • This is impossible as the numbers do not fit the formula! • (Possible money making opportunity?!)

  13. To draw prisms in 3D: • Draw the cross-section, using horizontal & vertical lines where possible • Draw depth lines from each possible corner, making sure they are equal in length and parallel • Use horizontal & vertical lines to connect the depth lines • Eg cube • Eg triangular prism

  14. Other 3D solids have unique ways of drawing them • Cylinder • Cone • Square-based pyramid • Draw an oval • Draw a rhombus • on an angle • Draw an oval • Add two sloping lines • Add two vertical lines • Add four sloping lines • Draw another oval

  15. 3D sketching • Make 3D sketches of the following solids: • Cube • Cuboid • Square-based pyramid • Triangular prism • Cylinder • Cone

  16. 3D sketching • Make 3D sketches of the following solids: • Cube • Cuboid • Square-based pyramid • Triangular prism • Cylinder • Cone

  17. Nets A net shows what a 3D solid could look like if ‘unfolded’ and laid out flat • Can you name the 3D solids with these nets? • Square-based pyramid • Triangular prism • Cylinder Cube

  18. 4. Using the grid provided with 1 square = 1 cm, draw an accurate net of these solids • 5cm • 2cm • 3cm • 6cm • 3cm • 4cm • 4cm

  19. Nets • 1. Match the 3D solids with their net

  20. Nets 2. The net is folded to make a cube.Two other vertices meet at P. Mark each of these vertices with the letter P. • 1. Match the 3D solids with their net • P • P • P 3. The net shown is folded to make a dodecahedron. Label the face which is opposite the shaded one • P

  21. Summary • We have learnt the names of some 3D shapes • We have investigated a link between their Faces, Edges and Vertices • We have aseen a formula linking these together. • We have learnt how to sketch 3D shapes • We have seen how to draw a net of 3D solids https://www.youtube.com/watch?v=uZ8Jy1xgqPU

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