Download presentation
Presentation is loading. Please wait.
1
Slideshow 44, Mathematics Mr Richard Sasaki Room 307
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 Note: Please bring scissors and glue from next lesson!
3
Some Simple 3-D Shapes Sphere Cylinder Cone 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 What is a plane?
A plane is a flat 2D surface usually thought to be infinite in length. π π π π΄ π π΅ π π· πΆ 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.
7
Example A coin is lifted up and down rapidly covering a height of 5 ππ. 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 cylinderβs lateral surface is produced. Cylinder 5 ππ The lateral surface is all parts of a shape excluding itβs base or bases.
8
6 ππ Cone 3 ππ 7 ππ Triangular Prism 2 ππ A prism (with bases congruent to the initial polygon) 4 ππ 3 ππ
9
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.
10
Some other definitions
What is an apex? An apex is thought of as the sharpest point of a shape. Itβs often at the top (like a peak). apex apex apex Shapes like these are most commonly associated with βapexβ.
11
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?
12
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.
Similar presentations
