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## Cones – Part 1

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**Cones – Part 1**Slideshow 47, Mathematics Mr Richard Sasaki Room 307**Understand the “net” of a cone and its properties**• Calculate radii, arc lengths and central angles for sectors and lateral surfaces of cones Objectives**Sphere**Some Simple 3-D Shapes Cone Cylinder Square-based pyramid Hemisphere**Platonic solids / Convex regular polyhedrons**Cube Tetrahedron Octahedron Dodecahedron Icosahedron**Prisms**Cuboid Hexagonal Prism Pentagonal Prism Triangular Prism Octagonal Prism Decagonal Prism Dodecagonal Prism Heptagonal 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? Lateral Surface(s) Base(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. Radius / Radii Central angle(s) (Area) Sector(s) (Area) 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? (Area) 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 . We divided the area by 2 because the central angle is 180o. How can we write the area in terms of a and r? Area =**Sectors**Sector Area (S) = (Area) Arc Length () = Example A sector has radius 3cm and central angle 90o. Calculate its area, S and arc length,. S = =**Answers**tall/thin wide can’t flat face When When**The Cone**As you know, this sector can be folded to make the lateral face of the cone. (Area) However, on a cone, some information will be represented differently. Slant height -**apex**base slant height circumference