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Exploring 3D Shapes Through Moving Planes: A Mathematical Perspective

This presentation, led by Mr. Richard Sasaki in Room 307, addresses the objectives of identifying common 3D shapes, understanding how moving planes can create these forms, and exploring solids of revolution. Students will learn about basic shapes like cylinders, cones, spheres, and prism variants, as well as more complex Platonic and concave polyhedra. The session includes a review of the concept of planes and their infinite nature, as well as engaging exercises to visualize and create 3D shapes through movement, enhancing spatial understanding and mathematical skills.

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Exploring 3D Shapes Through Moving Planes: A Mathematical Perspective

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Presentation Transcript

  1. Moving Planes Slideshow 44, Mathematics Mr Richard Sasaki Room 307

  2. Objectives Recall names of some common 3d Shapes Understand how moving planes form 3D shapes Understand solids of revolution

  3. Some Simple 3-D Shapes Cylinder Cone Sphere Square-based pyramid Hemisphere

  4. Platonic solids / concave regular polyhedrons Cube Tetrahedron Octahedron Dodecahedron Icosahedron

  5. Prisms Triangular Prism Cuboid Pentagonal Prism Hexagonal Prism Heptagonal Prism Dodecagonal Prism

  6. Planes - Review A plane is a flat 2D surface thought to be infinite in length. If a finite plane moves rapidly, it can create the form of a 3D object. Similarly, if we trace the movement of the object it can do the same. What is a plane?

  7. Example A coin is lifted up and down rapidly covering a height of 5cm. If the centre of the coin remains as the centre of the base of the 3D shape, state the shape produced and draw it. Lateral surface – All of the surface except for the base(s) 5 cm Cylinder

  8. Answers A prism with bases congruent to the initial polygon Cone 6 cm 3 cm 4 cm 3 cm 7 cm Triangular Prism 2 cm

  9. Some other definitions Legs are two of the edges of a right-angled triangle. Hypotenuse What is a leg? Legs Note: Leg is only used with right-angled triangles. Not with other triangles.

  10. Some other definitions An apex is thought of as the sharpest point of a shape. It’s often at the top (like a peak). apex apex apex What is an apex? Shapes like these are most commonly associated with “apex”.

  11. Some other definitions solid of revolution We call this a . In Question 1 on the last worksheet, we had an example where a 3D shape is produced by spinning a polygon about an edge of it. We will think of a solid of revolution has being based around its vertical centre.

  12. Some other definitions Let’s try to think about other shapes! If we connect a semi-circle to the central line of revolution, what shape will appear?

  13. Answers Sphere Hemisphere Rectangle Right-angled triangle The distance from the central line of revolution must be the same horizontally about every part of the solid.

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