1 / 14

Cones – Part 1

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.

kylee-patterson
Télécharger la présentation

Cones – Part 1

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

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

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

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

  4. Platonic solids / Convex regular polyhedrons Cube Tetrahedron Octahedron Dodecahedron Icosahedron

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

  6. 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)

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

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

  9. 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 =

  10. 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 =

  11. 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 = =

  12. Answers tall/thin wide can’t flat face When When

  13. 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 -

  14. apex base slant height circumference

More Related