1 / 12

12-6: Surface Areas of Cones

12-6: Surface Areas of Cones. By: John Cao & Colby Le. Objectives:. Find lateral areas of cones Find surface areas of cones. Characteristics of Cones:. A cone’s base is a circle and its vertex is referred to as point V.

koren
Download Presentation

12-6: Surface Areas of Cones

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. 12-6: Surface Areas of Cones By: John Cao & Colby Le

  2. Objectives: • Find lateral areas of cones • Find surface areas of cones

  3. Characteristics of Cones: • A cone’s base is a circle and its vertex is referred to as point V. • The axis of a cone is the segment with endpoints at the vertex and the center of the base. • A segment that has one endpoint at the vertex and is perpendicular to the base is called the altitude of the cone.

  4. Characteristics of Cones cont’d: • Right Cone - A cone that has an altitude that is also it’s axis. • Oblique Cone – A cone that has an altitude that is not it’s axis. • The measure of any segment from the vertex of a right cone to the edge of the base is the slant height, l. • The measure of the altitude is the height, h.

  5. Lateral Area of a Cone • The lateral area of a cone is the sector of a circle with radius l, the slant height of the cone. • The arc length of the sector of the circle is the same as the circumference of the base, or 2πr. • The circumference of the circle containing the sector is 2πl. • Using this information, you can create a formula to find the lateral area of the cone. • Formula: area of sector = πrl

  6. Example 1 1.) If you have a cone whose base radius is 5 units and it’s slant height is 10 units, find the lateral area of the cone. Round to the nearest tenth. area of sector = πrl area of sector = π(5)(10) a.) area of sector ~ 157.1 units2

  7. Your Turn: • A cone has a base radius of 8 units and a slant height of 6 units. What is the lateral area of that cone to the nearest tenth? a.) area of sector ~ 150.8 units2

  8. Surface Area of a Cone • The total surface area of a cone is represented by T. • To find the surface area of a cone, add the area of the base to the lateral area of the cone. • Formula: T = πrl+ πr2

  9. Example 2 2.) Find the surface area of a cone if its base radius is 3 units and its slant height is 4 units. Round to the nearest tenth. T = πrl+ πr2 T = π(3)(4) + π(3)2 a.) T ~ 66.0 units2

  10. Your Turn: • A cone has a slant height of 7 units and a base radius of 5 units. Find the surface area of the cone to the nearest tenth. a.) T ~ 188.5 units2

  11. Your Turn: • Find the surface area of a cone to the nearest tenth if it has a base radius of 2 and a slant height of 13. a.) T ~ 94.2 units2

  12. Assignment page 668-669 #7-22

More Related