Cones – Part 1 Slideshow 47, Mathematics Mr Richard Sasaki Room 307

Objectives Understand the “net” of a cone and its properties Calculate radii, arc lengths and central angles for sectors and lateral surfaces of cones

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

Platonic solids / Convex regular polyhedrons Tetrahedron Cube Octahedron Dodecahedron Icosahedron

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

The Net for a Cone We know why a true net for a cone can’t be made…right? It connects at a point with zero size. But what would it look like? Base(s) Lateral Surface(s)

The Net for a Cone Let’s look at some cone properties. What will each cone look like? (Thanks Isamu for your help here.)

The Net for a Cone Let’s look at the lateral surfaces. Sector(s) Radius / Radii Central angle(s) Arc Length

Sectors Have a look at the sector below. This would be the cone’s lateral surface. How do we calculate its area and arc length? For a regular circle… Area = Circumference =

Sectors Area = Circumference = If we thought of a circle as a sector, it has a central angle of and an arc length of. A semi-circle would have a central angle of and an arc length of. Area = We divided the area by 2 because the central angle is 180 o. How can we write the area in terms of a and r?

Sectors Sector Area (S) = Example S =

Answers tall/thin wide can’t flat face

The Cone As you know, this sector can be folded to make the lateral face of the cone. However, on a cone, some information will be represented differently.

apex base slantheight circumference