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

Objectives Recall names of some common 3D Shapes Understand how moving planes form 3D shapes Understand solids of revolution Note: Please bring scissors and glue from next lesson!

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

Platonic Solids / Concave regular polyhedrons Cube Tetrahedron Octahedron Dodecahedron Icosahedron

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

Planes - Review What is a plane? A plane is a flat 2D surface usually thought to be infinite in length. 𝑞 𝑍 𝑌 𝐴 𝑝 𝐵 𝑋 𝐷 𝐶 If a finite sized plane moves rapidly, it can create the form of a 3D object. Similarly, if we trace the movement of the object it can produce the same thing.

Example A coin is lifted up and down rapidly covering a height of 5 𝑐𝑚. If the centre of the coin remains as the centre of the base of the 3D shape, state the shape produced and draw it. Here, the cylinder’s lateral surface is produced. Cylinder 5 𝑐𝑚 The lateral surface is all parts of a shape excluding it’s base or bases.

6 𝑐𝑚 Cone 3 𝑐𝑚 7 𝑐𝑚 Triangular Prism 2 𝑐𝑚 A prism (with bases congruent to the initial polygon) 4 𝑐𝑚 3 𝑐𝑚

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

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

Some other definitions Before, we saw a question where a 3D shape is formed by spinning a 2D shape about an edge of it. We call this a . solid of revolution We will think of a solid of revolution as being based around its vertical centre. If we connect a semi-circle to the central line of revolution, what shape will appear?

Cylinder Hemisphere Semicircle Right-Angled Triangle If the edge of something spins, this forms a circle. That means there will be a curved face. Something like this would be fine.