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Transcript of Volume of Geometric Solids Geometry Regular Program SY 2014-2015 Sources: Discovering Geometry...
![Page 1: Volume of Geometric Solids Geometry Regular Program SY 2014-2015 Sources: Discovering Geometry (2008) by Michael Serra Geometry (2007) by Ron Larson.](https://reader030.fdocuments.us/reader030/viewer/2022032723/56649d095503460f949db04b/html5/thumbnails/1.jpg)
Volume of Geometric Solids
Geometry Regular ProgramSY 2014-2015
Sources:
Discovering Geometry (2008) by Michael Serra
Geometry (2007) by Ron Larson
![Page 2: Volume of Geometric Solids Geometry Regular Program SY 2014-2015 Sources: Discovering Geometry (2008) by Michael Serra Geometry (2007) by Ron Larson.](https://reader030.fdocuments.us/reader030/viewer/2022032723/56649d095503460f949db04b/html5/thumbnails/2.jpg)
The Geometric Solids
These solids take up space.
What is VOLUME?
It refers to the measure of
the amount of space
contained in a solid.
![Page 3: Volume of Geometric Solids Geometry Regular Program SY 2014-2015 Sources: Discovering Geometry (2008) by Michael Serra Geometry (2007) by Ron Larson.](https://reader030.fdocuments.us/reader030/viewer/2022032723/56649d095503460f949db04b/html5/thumbnails/3.jpg)
The Geometric SolidsWhat is
VOLUME?
It refers to the measure of
the amount of space
contained in a solid.
It is measured in cubic units.
![Page 4: Volume of Geometric Solids Geometry Regular Program SY 2014-2015 Sources: Discovering Geometry (2008) by Michael Serra Geometry (2007) by Ron Larson.](https://reader030.fdocuments.us/reader030/viewer/2022032723/56649d095503460f949db04b/html5/thumbnails/4.jpg)
Example:
How many cubes of cubic unit can fit inside the solid?
![Page 5: Volume of Geometric Solids Geometry Regular Program SY 2014-2015 Sources: Discovering Geometry (2008) by Michael Serra Geometry (2007) by Ron Larson.](https://reader030.fdocuments.us/reader030/viewer/2022032723/56649d095503460f949db04b/html5/thumbnails/5.jpg)
Example:
How many cubes of cubic unit can fit inside the solid?
![Page 6: Volume of Geometric Solids Geometry Regular Program SY 2014-2015 Sources: Discovering Geometry (2008) by Michael Serra Geometry (2007) by Ron Larson.](https://reader030.fdocuments.us/reader030/viewer/2022032723/56649d095503460f949db04b/html5/thumbnails/6.jpg)
Example:
How many cubes of cubic unit can fit inside the solid?
![Page 7: Volume of Geometric Solids Geometry Regular Program SY 2014-2015 Sources: Discovering Geometry (2008) by Michael Serra Geometry (2007) by Ron Larson.](https://reader030.fdocuments.us/reader030/viewer/2022032723/56649d095503460f949db04b/html5/thumbnails/7.jpg)
So how do we determine the volume of a solid?
It takes 3x3 cubes to cover the base area.
It takes 3x the base area to fill up the whole solid.
You need the base area h times. Base area
Height h
![Page 8: Volume of Geometric Solids Geometry Regular Program SY 2014-2015 Sources: Discovering Geometry (2008) by Michael Serra Geometry (2007) by Ron Larson.](https://reader030.fdocuments.us/reader030/viewer/2022032723/56649d095503460f949db04b/html5/thumbnails/8.jpg)
VOLUME OF SOLIDS
PRISMV = Base area x Height of prism
CYLINDERV = Base area x Height of cylinder
![Page 9: Volume of Geometric Solids Geometry Regular Program SY 2014-2015 Sources: Discovering Geometry (2008) by Michael Serra Geometry (2007) by Ron Larson.](https://reader030.fdocuments.us/reader030/viewer/2022032723/56649d095503460f949db04b/html5/thumbnails/9.jpg)
Exercises on VolumeSolve for the volume of each solid
![Page 10: Volume of Geometric Solids Geometry Regular Program SY 2014-2015 Sources: Discovering Geometry (2008) by Michael Serra Geometry (2007) by Ron Larson.](https://reader030.fdocuments.us/reader030/viewer/2022032723/56649d095503460f949db04b/html5/thumbnails/10.jpg)
Exercises on VolumeSolve for the volume of each solid
![Page 11: Volume of Geometric Solids Geometry Regular Program SY 2014-2015 Sources: Discovering Geometry (2008) by Michael Serra Geometry (2007) by Ron Larson.](https://reader030.fdocuments.us/reader030/viewer/2022032723/56649d095503460f949db04b/html5/thumbnails/11.jpg)
Exercises on VolumeSolve for the volume of each solid
![Page 12: Volume of Geometric Solids Geometry Regular Program SY 2014-2015 Sources: Discovering Geometry (2008) by Michael Serra Geometry (2007) by Ron Larson.](https://reader030.fdocuments.us/reader030/viewer/2022032723/56649d095503460f949db04b/html5/thumbnails/12.jpg)
Try these!Which has a greater volume?
![Page 13: Volume of Geometric Solids Geometry Regular Program SY 2014-2015 Sources: Discovering Geometry (2008) by Michael Serra Geometry (2007) by Ron Larson.](https://reader030.fdocuments.us/reader030/viewer/2022032723/56649d095503460f949db04b/html5/thumbnails/13.jpg)
Try these!Which has a greater volume?
![Page 14: Volume of Geometric Solids Geometry Regular Program SY 2014-2015 Sources: Discovering Geometry (2008) by Michael Serra Geometry (2007) by Ron Larson.](https://reader030.fdocuments.us/reader030/viewer/2022032723/56649d095503460f949db04b/html5/thumbnails/14.jpg)
Try these!Which has a greater volume?
![Page 15: Volume of Geometric Solids Geometry Regular Program SY 2014-2015 Sources: Discovering Geometry (2008) by Michael Serra Geometry (2007) by Ron Larson.](https://reader030.fdocuments.us/reader030/viewer/2022032723/56649d095503460f949db04b/html5/thumbnails/15.jpg)
Try these!Solve for the volume of each solid
![Page 16: Volume of Geometric Solids Geometry Regular Program SY 2014-2015 Sources: Discovering Geometry (2008) by Michael Serra Geometry (2007) by Ron Larson.](https://reader030.fdocuments.us/reader030/viewer/2022032723/56649d095503460f949db04b/html5/thumbnails/16.jpg)
Try these!Solve for the volume of each solid
![Page 17: Volume of Geometric Solids Geometry Regular Program SY 2014-2015 Sources: Discovering Geometry (2008) by Michael Serra Geometry (2007) by Ron Larson.](https://reader030.fdocuments.us/reader030/viewer/2022032723/56649d095503460f949db04b/html5/thumbnails/17.jpg)
How about the volume of a pyramid?
https://www.youtube.com/watch?v=OUDjY6vJ8pw
![Page 18: Volume of Geometric Solids Geometry Regular Program SY 2014-2015 Sources: Discovering Geometry (2008) by Michael Serra Geometry (2007) by Ron Larson.](https://reader030.fdocuments.us/reader030/viewer/2022032723/56649d095503460f949db04b/html5/thumbnails/18.jpg)
VOLUME OF SOLIDS
PYRAMIDV = One-third of the volume of the prism with same base and height
![Page 19: Volume of Geometric Solids Geometry Regular Program SY 2014-2015 Sources: Discovering Geometry (2008) by Michael Serra Geometry (2007) by Ron Larson.](https://reader030.fdocuments.us/reader030/viewer/2022032723/56649d095503460f949db04b/html5/thumbnails/19.jpg)
How about the volume of a cone?
https://www.youtube.com/watch?v=0ZACAU4SGyM
![Page 20: Volume of Geometric Solids Geometry Regular Program SY 2014-2015 Sources: Discovering Geometry (2008) by Michael Serra Geometry (2007) by Ron Larson.](https://reader030.fdocuments.us/reader030/viewer/2022032723/56649d095503460f949db04b/html5/thumbnails/20.jpg)
VOLUME OF SOLIDS
CONEV = One-third of the volume of the cylinder with same base & height
![Page 21: Volume of Geometric Solids Geometry Regular Program SY 2014-2015 Sources: Discovering Geometry (2008) by Michael Serra Geometry (2007) by Ron Larson.](https://reader030.fdocuments.us/reader030/viewer/2022032723/56649d095503460f949db04b/html5/thumbnails/21.jpg)
VOLUME
PRISM x
CYLINDER
x
PYRAMID
x
CONE x
SUMMARY: VOLUME
![Page 22: Volume of Geometric Solids Geometry Regular Program SY 2014-2015 Sources: Discovering Geometry (2008) by Michael Serra Geometry (2007) by Ron Larson.](https://reader030.fdocuments.us/reader030/viewer/2022032723/56649d095503460f949db04b/html5/thumbnails/22.jpg)
Exercises on VolumeSolve for the volume of each solid
![Page 23: Volume of Geometric Solids Geometry Regular Program SY 2014-2015 Sources: Discovering Geometry (2008) by Michael Serra Geometry (2007) by Ron Larson.](https://reader030.fdocuments.us/reader030/viewer/2022032723/56649d095503460f949db04b/html5/thumbnails/23.jpg)
Exercises on VolumeSolve for the volume of each solid
![Page 24: Volume of Geometric Solids Geometry Regular Program SY 2014-2015 Sources: Discovering Geometry (2008) by Michael Serra Geometry (2007) by Ron Larson.](https://reader030.fdocuments.us/reader030/viewer/2022032723/56649d095503460f949db04b/html5/thumbnails/24.jpg)
Exercises on VolumeSolve for the volume of each solid
![Page 25: Volume of Geometric Solids Geometry Regular Program SY 2014-2015 Sources: Discovering Geometry (2008) by Michael Serra Geometry (2007) by Ron Larson.](https://reader030.fdocuments.us/reader030/viewer/2022032723/56649d095503460f949db04b/html5/thumbnails/25.jpg)
Extra Exercises on VolumeSolve for the volume of each given solid
![Page 26: Volume of Geometric Solids Geometry Regular Program SY 2014-2015 Sources: Discovering Geometry (2008) by Michael Serra Geometry (2007) by Ron Larson.](https://reader030.fdocuments.us/reader030/viewer/2022032723/56649d095503460f949db04b/html5/thumbnails/26.jpg)
Extra Exercises on VolumeSolve for the volume of each given solid
![Page 27: Volume of Geometric Solids Geometry Regular Program SY 2014-2015 Sources: Discovering Geometry (2008) by Michael Serra Geometry (2007) by Ron Larson.](https://reader030.fdocuments.us/reader030/viewer/2022032723/56649d095503460f949db04b/html5/thumbnails/27.jpg)
Extra Exercises on VolumeSolve for the volume of each given solid
![Page 28: Volume of Geometric Solids Geometry Regular Program SY 2014-2015 Sources: Discovering Geometry (2008) by Michael Serra Geometry (2007) by Ron Larson.](https://reader030.fdocuments.us/reader030/viewer/2022032723/56649d095503460f949db04b/html5/thumbnails/28.jpg)
Extra Exercises on VolumeSolve for the volume of each given solid
![Page 29: Volume of Geometric Solids Geometry Regular Program SY 2014-2015 Sources: Discovering Geometry (2008) by Michael Serra Geometry (2007) by Ron Larson.](https://reader030.fdocuments.us/reader030/viewer/2022032723/56649d095503460f949db04b/html5/thumbnails/29.jpg)
Extra Exercises on VolumeSolve for the volume of the liquid.
![Page 30: Volume of Geometric Solids Geometry Regular Program SY 2014-2015 Sources: Discovering Geometry (2008) by Michael Serra Geometry (2007) by Ron Larson.](https://reader030.fdocuments.us/reader030/viewer/2022032723/56649d095503460f949db04b/html5/thumbnails/30.jpg)
Extra Exercises on VolumeSolve for the volume of the liquid.
![Page 31: Volume of Geometric Solids Geometry Regular Program SY 2014-2015 Sources: Discovering Geometry (2008) by Michael Serra Geometry (2007) by Ron Larson.](https://reader030.fdocuments.us/reader030/viewer/2022032723/56649d095503460f949db04b/html5/thumbnails/31.jpg)
Extra Exercises on Volume
![Page 32: Volume of Geometric Solids Geometry Regular Program SY 2014-2015 Sources: Discovering Geometry (2008) by Michael Serra Geometry (2007) by Ron Larson.](https://reader030.fdocuments.us/reader030/viewer/2022032723/56649d095503460f949db04b/html5/thumbnails/32.jpg)
Extra Exercises on Volume (seatwork) Solve the following:
1. Find the volume of an oblique prism inclined 45o from the base, if the area of the base is 20 cm2
and the lateral edge is 15 cm.
2. Find the volume of a right cylinder with a cylindrical hole if the larger radius is 10 inches, the smaller radius is 8 inches and the height is 9 inches.