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

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Moving planes

Moving Planes

Slideshow 44, Mathematics

Mr Richard Sasaki

Room 307


Objectives

Objectives

Recall names of some common 3d Shapes

Understand how moving planes form 3D shapes

Understand solids of revolution


Some simple 3 d shapes

Some Simple 3-D Shapes

Cylinder

Cone

Sphere

Square-based pyramid

Hemisphere


Platonic solids concave regular polyhedrons

Platonic solids / concave regular polyhedrons

Cube

Tetrahedron

Octahedron

Dodecahedron

Icosahedron


Prisms

Prisms

Triangular Prism

Cuboid

Pentagonal Prism

Hexagonal Prism

Heptagonal Prism

Dodecagonal Prism


Planes review

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?


Example

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


Answers

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


Some other definitions

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.


Some other definitions1

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”.


Some other definitions2

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.


Some other definitions3

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?


Answers1

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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