12.3 surface areas of pyramids and cones goals students ......gh lesson 12 3_notes.notebook march...
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GHLesson 123_notes.notebook March 29, 2016
12.3 Surface Areas of Pyramids and Cones
Goals
Students will be able to . . .
• find lateral areas and surface areas of pyramids.
• find lateral areas and surface areas of cones.
Pyramid 3D object in which one face can be any polygon and the other faces are triangles that meet at a common vertex.
Base can be any polygon
Lateral faces faces that are not the base (triangles)
Lateral faces will be isosceles triangles if the base is a regular polygon.
GHLesson 123_notes.notebook March 29, 2016
HeightSlantheighth l
Vertex the point where all the lateral faces meet
Height (h) perpendicular distance from the vertex to the base
When the pyramid is a right pyramid the altitude connects the vertex and center of the base.
Slant height (l ) the height of a lateral face (triangle) of the pyramid
Square pyramid
Square Base
Right Triangle May need to use Pythagorean Theorem, Trigonometry or Special Right Triangles to find an unknown dimension.
GHLesson 123_notes.notebook March 29, 2016
ss
ss
l
l
ll
Using the net of a pyramid, find the equation for the Lateral Area.
L =
1 2
S = pl + B
Vertex
Altitude
Base edge
Lateral edge
lRegular Hexagonal Pyramid
GHLesson 123_notes.notebook March 29, 2016
Cone is a solid with a circular base and a vertex (there are no polygons).
Height (right cone) the perpendicular distance from the vertex to the center of the base.
Slant height the distance from the vertex to any point on the edge of the base.
S = πrl + B
GHLesson 123_notes.notebook March 29, 2016
Practice 123
GHLesson 123_notes.notebook March 29, 2016
GHLesson 123_notes.notebook March 29, 2016