Moving Planes

Slideshow 44, MathematicsMr 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

Sphere Cylinder Cone

Square-based pyramid

Hemisphere

Platonic Solids / Concave regular polyhedrons

Tetrahedron Cube Octahedron

Dodecahedron Icosahedron

Prisms

CuboidTriangular Prism

Pentagonal Prism

Hexagonal Prism

Heptagonal Prism

Dodecagonal Prism

Planes - ReviewWhat is a plane?A plane is a flat 2D surface usually thought to be infinite in length.

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.

𝑝𝐴 𝐵𝐷 𝐶

𝑞𝑍 𝑌𝑋

ExampleA coin is lifted up and down rapidly covering a height of . If the centre of the coin remains as the centre of the base of the 3D shape, state the shape produced and draw it.

Cylinder 5𝑐𝑚Here, the cylinder’s lateral surface is produced.The lateral surface is all parts of a shape excluding it’s base or bases.

Answers

Cone6𝑐𝑚3𝑐𝑚

Triangular Prism

7𝑐𝑚2𝑐𝑚

A prism (with bases congruent to the initial polygon)

3𝑐𝑚4𝑐𝑚

Some other definitionsWhat is a leg?Legs are two of the edges of a right-angled triangle.

LegsHypotenuse

Note: The word leg is only used with right-angled triangles. Not with other triangles.

Some other definitionsWhat 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 definitionsBefore, 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 revolutionWe 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?

Let’s think about other shapes too!

Answers1. Cylinder2. Hemisphere3. Semicircle4. Right-angled triangle5. The distance from the central line of

revolution will act as a radius of what is being spun.

Or….we didn’t raise the shape.