unit 4: exploring three dimensional figures · unit 4 day 1 notes.notebook may 06, 2014 review:...
TRANSCRIPT
![Page 1: Unit 4: Exploring Three Dimensional Figures · unit 4 day 1 notes.notebook May 06, 2014 Review: Area of a Triangle: 1/2 b*h Area of a Rectangle/Square: l*w Area of a Parallelogram:](https://reader033.vdocuments.mx/reader033/viewer/2022050200/5f53b141abb5b52d04213555/html5/thumbnails/1.jpg)
unit 4 day 1 notes.notebook May 06, 2014
Unit 4: Exploring ThreeDimensional Figures
![Page 2: Unit 4: Exploring Three Dimensional Figures · unit 4 day 1 notes.notebook May 06, 2014 Review: Area of a Triangle: 1/2 b*h Area of a Rectangle/Square: l*w Area of a Parallelogram:](https://reader033.vdocuments.mx/reader033/viewer/2022050200/5f53b141abb5b52d04213555/html5/thumbnails/2.jpg)
unit 4 day 1 notes.notebook May 06, 2014
Cylindera solid with congruent circular bases in a pair of parallel planes
Cone has a circular base and a vertex
![Page 3: Unit 4: Exploring Three Dimensional Figures · unit 4 day 1 notes.notebook May 06, 2014 Review: Area of a Triangle: 1/2 b*h Area of a Rectangle/Square: l*w Area of a Parallelogram:](https://reader033.vdocuments.mx/reader033/viewer/2022050200/5f53b141abb5b52d04213555/html5/thumbnails/3.jpg)
unit 4 day 1 notes.notebook May 06, 2014
Sphere a set of points in space that are a given distance from a given point.
Prism a polyhedron with two congruent faces that are polygons contained in parallel planes
The two parallel faces are called bases of the prism.
The other faces are called lateral faces, and are shaped like parallelograms
A regular prism is a prism whose bases are regular polygons
![Page 4: Unit 4: Exploring Three Dimensional Figures · unit 4 day 1 notes.notebook May 06, 2014 Review: Area of a Triangle: 1/2 b*h Area of a Rectangle/Square: l*w Area of a Parallelogram:](https://reader033.vdocuments.mx/reader033/viewer/2022050200/5f53b141abb5b52d04213555/html5/thumbnails/4.jpg)
unit 4 day 1 notes.notebook May 06, 2014
Pyramid
http://www.mathsnet.net/geometry/solid/pyramids.html
a polyhedron that has all faces except one intersecting at one point
One base
All faces are triangles
All faces meet at an endpoint (vertex)
Surface Area
Surface Area: the sum of the areas of its outer surfaces
![Page 5: Unit 4: Exploring Three Dimensional Figures · unit 4 day 1 notes.notebook May 06, 2014 Review: Area of a Triangle: 1/2 b*h Area of a Rectangle/Square: l*w Area of a Parallelogram:](https://reader033.vdocuments.mx/reader033/viewer/2022050200/5f53b141abb5b52d04213555/html5/thumbnails/5.jpg)
unit 4 day 1 notes.notebook May 06, 2014
Review:
Area of a Triangle: 1/2 b*h
Area of a Rectangle/Square: l*w
Area of a Parallelogram: b*h
Area of a Trapezoid: 1/2*h*(b1 + b2)
Regular square pyramid- a square pyramid with congruent triangular faces
12 in.
10 in.
Find the surface area:
Area of base:
Area of faces (4):
Example 1
![Page 6: Unit 4: Exploring Three Dimensional Figures · unit 4 day 1 notes.notebook May 06, 2014 Review: Area of a Triangle: 1/2 b*h Area of a Rectangle/Square: l*w Area of a Parallelogram:](https://reader033.vdocuments.mx/reader033/viewer/2022050200/5f53b141abb5b52d04213555/html5/thumbnails/6.jpg)
unit 4 day 1 notes.notebook May 06, 2014
4
3
5
6
Find the surface area of the triangular prism. bottom:
front:
back:
bases:
Example 2
![Page 7: Unit 4: Exploring Three Dimensional Figures · unit 4 day 1 notes.notebook May 06, 2014 Review: Area of a Triangle: 1/2 b*h Area of a Rectangle/Square: l*w Area of a Parallelogram:](https://reader033.vdocuments.mx/reader033/viewer/2022050200/5f53b141abb5b52d04213555/html5/thumbnails/7.jpg)
unit 4 day 1 notes.notebook May 06, 2014
2.
3.
![Page 8: Unit 4: Exploring Three Dimensional Figures · unit 4 day 1 notes.notebook May 06, 2014 Review: Area of a Triangle: 1/2 b*h Area of a Rectangle/Square: l*w Area of a Parallelogram:](https://reader033.vdocuments.mx/reader033/viewer/2022050200/5f53b141abb5b52d04213555/html5/thumbnails/8.jpg)
unit 4 day 1 notes.notebook May 06, 2014
4.
Try These5. 6.
![Page 9: Unit 4: Exploring Three Dimensional Figures · unit 4 day 1 notes.notebook May 06, 2014 Review: Area of a Triangle: 1/2 b*h Area of a Rectangle/Square: l*w Area of a Parallelogram:](https://reader033.vdocuments.mx/reader033/viewer/2022050200/5f53b141abb5b52d04213555/html5/thumbnails/9.jpg)
unit 4 day 1 notes.notebook May 06, 2014
Surface Area of Cylinders, Cones, and Spheres
CylinderSA = 2πrh + 2πr2
h
r
Cone SA = πrs + πr2
slant height(s)
r
h
![Page 10: Unit 4: Exploring Three Dimensional Figures · unit 4 day 1 notes.notebook May 06, 2014 Review: Area of a Triangle: 1/2 b*h Area of a Rectangle/Square: l*w Area of a Parallelogram:](https://reader033.vdocuments.mx/reader033/viewer/2022050200/5f53b141abb5b52d04213555/html5/thumbnails/10.jpg)
unit 4 day 1 notes.notebook May 06, 2014
SphereSA = 4πr2
r
Example 710
30
![Page 11: Unit 4: Exploring Three Dimensional Figures · unit 4 day 1 notes.notebook May 06, 2014 Review: Area of a Triangle: 1/2 b*h Area of a Rectangle/Square: l*w Area of a Parallelogram:](https://reader033.vdocuments.mx/reader033/viewer/2022050200/5f53b141abb5b52d04213555/html5/thumbnails/11.jpg)
unit 4 day 1 notes.notebook May 06, 2014
Example 8
5 cm
7 cm
Example 94 m
10 m
![Page 12: Unit 4: Exploring Three Dimensional Figures · unit 4 day 1 notes.notebook May 06, 2014 Review: Area of a Triangle: 1/2 b*h Area of a Rectangle/Square: l*w Area of a Parallelogram:](https://reader033.vdocuments.mx/reader033/viewer/2022050200/5f53b141abb5b52d04213555/html5/thumbnails/12.jpg)
unit 4 day 1 notes.notebook May 06, 2014
Example 10
10 m