SPHERES Surface Area and Volume Geometry Regular Program SY 2014-2015 Sources: Discovering Geometry...
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Transcript of SPHERES Surface Area and Volume Geometry Regular Program SY 2014-2015 Sources: Discovering Geometry...
![Page 1: SPHERES Surface Area and Volume Geometry Regular Program SY 2014-2015 Sources: Discovering Geometry (2008) by Michael Serra Geometry (2007) by Ron Larson.](https://reader030.fdocuments.us/reader030/viewer/2022033105/56649d885503460f94a6d1c0/html5/thumbnails/1.jpg)
SPHERESSurface Area and Volume
Geometry Regular ProgramSY 2014-2015
Sources:
Discovering Geometry (2008) by Michael Serra
Geometry (2007) by Ron Larson
![Page 2: SPHERES Surface Area and Volume Geometry Regular Program SY 2014-2015 Sources: Discovering Geometry (2008) by Michael Serra Geometry (2007) by Ron Larson.](https://reader030.fdocuments.us/reader030/viewer/2022033105/56649d885503460f94a6d1c0/html5/thumbnails/2.jpg)
The Geometric Solids
![Page 3: SPHERES Surface Area and Volume Geometry Regular Program SY 2014-2015 Sources: Discovering Geometry (2008) by Michael Serra Geometry (2007) by Ron Larson.](https://reader030.fdocuments.us/reader030/viewer/2022033105/56649d885503460f94a6d1c0/html5/thumbnails/3.jpg)
SPHERE
![Page 4: SPHERES Surface Area and Volume Geometry Regular Program SY 2014-2015 Sources: Discovering Geometry (2008) by Michael Serra Geometry (2007) by Ron Larson.](https://reader030.fdocuments.us/reader030/viewer/2022033105/56649d885503460f94a6d1c0/html5/thumbnails/4.jpg)
HEMISPHERE: Half a sphere PLUS the circular base
The circle that encloses the base
is the GREAT CIRCLE.
If you were to slice a pingpong ball, where do you slice it to get the largest circular cross-
section?
If a plane cuts a sphere along the center, then the
plane contains the great circle.
Is the equator In a globe a great circle?
![Page 5: SPHERES Surface Area and Volume Geometry Regular Program SY 2014-2015 Sources: Discovering Geometry (2008) by Michael Serra Geometry (2007) by Ron Larson.](https://reader030.fdocuments.us/reader030/viewer/2022033105/56649d885503460f94a6d1c0/html5/thumbnails/5.jpg)
How do we obtain the Volume of a sphere?
https://www.youtube.com/watch?v=h4j8l3p22e8
Video 1
![Page 6: SPHERES Surface Area and Volume Geometry Regular Program SY 2014-2015 Sources: Discovering Geometry (2008) by Michael Serra Geometry (2007) by Ron Larson.](https://reader030.fdocuments.us/reader030/viewer/2022033105/56649d885503460f94a6d1c0/html5/thumbnails/6.jpg)
How do we obtain the Volume of a sphere?
https://www.youtube.com/watch?v=YNutS8eIhEs
Video 2
![Page 7: SPHERES Surface Area and Volume Geometry Regular Program SY 2014-2015 Sources: Discovering Geometry (2008) by Michael Serra Geometry (2007) by Ron Larson.](https://reader030.fdocuments.us/reader030/viewer/2022033105/56649d885503460f94a6d1c0/html5/thumbnails/7.jpg)
Volume of a Sphere
Volume of a sphere
with radius r
![Page 8: SPHERES Surface Area and Volume Geometry Regular Program SY 2014-2015 Sources: Discovering Geometry (2008) by Michael Serra Geometry (2007) by Ron Larson.](https://reader030.fdocuments.us/reader030/viewer/2022033105/56649d885503460f94a6d1c0/html5/thumbnails/8.jpg)
Example:
![Page 9: SPHERES Surface Area and Volume Geometry Regular Program SY 2014-2015 Sources: Discovering Geometry (2008) by Michael Serra Geometry (2007) by Ron Larson.](https://reader030.fdocuments.us/reader030/viewer/2022033105/56649d885503460f94a6d1c0/html5/thumbnails/9.jpg)
How do we obtain the Surface Area of a sphere?
https://www.youtube.com/watch?v=cAxHYFRx1Fs
Video 3
![Page 10: SPHERES Surface Area and Volume Geometry Regular Program SY 2014-2015 Sources: Discovering Geometry (2008) by Michael Serra Geometry (2007) by Ron Larson.](https://reader030.fdocuments.us/reader030/viewer/2022033105/56649d885503460f94a6d1c0/html5/thumbnails/10.jpg)
How do we obtain the Surface Area of a sphere?
Video 4
https://www.youtube.com/watch?v=xuPl_8o_j7k
![Page 11: SPHERES Surface Area and Volume Geometry Regular Program SY 2014-2015 Sources: Discovering Geometry (2008) by Michael Serra Geometry (2007) by Ron Larson.](https://reader030.fdocuments.us/reader030/viewer/2022033105/56649d885503460f94a6d1c0/html5/thumbnails/11.jpg)
How do we obtain the Surface Area of a sphere?
![Page 12: SPHERES Surface Area and Volume Geometry Regular Program SY 2014-2015 Sources: Discovering Geometry (2008) by Michael Serra Geometry (2007) by Ron Larson.](https://reader030.fdocuments.us/reader030/viewer/2022033105/56649d885503460f94a6d1c0/html5/thumbnails/12.jpg)
Surface Area of a Sphere
Surface Area of a sphere
with radius r
How many circle areas cover the
sphere?
![Page 13: SPHERES Surface Area and Volume Geometry Regular Program SY 2014-2015 Sources: Discovering Geometry (2008) by Michael Serra Geometry (2007) by Ron Larson.](https://reader030.fdocuments.us/reader030/viewer/2022033105/56649d885503460f94a6d1c0/html5/thumbnails/13.jpg)
Example:
![Page 14: SPHERES Surface Area and Volume Geometry Regular Program SY 2014-2015 Sources: Discovering Geometry (2008) by Michael Serra Geometry (2007) by Ron Larson.](https://reader030.fdocuments.us/reader030/viewer/2022033105/56649d885503460f94a6d1c0/html5/thumbnails/14.jpg)
Sphere
Surface AreaVolume
Given a sphere with radius r
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Solve for the VOLUME and Surface Area:
![Page 16: SPHERES Surface Area and Volume Geometry Regular Program SY 2014-2015 Sources: Discovering Geometry (2008) by Michael Serra Geometry (2007) by Ron Larson.](https://reader030.fdocuments.us/reader030/viewer/2022033105/56649d885503460f94a6d1c0/html5/thumbnails/16.jpg)
Solve for the VOLUME and Surface Area:
![Page 17: SPHERES Surface Area and Volume Geometry Regular Program SY 2014-2015 Sources: Discovering Geometry (2008) by Michael Serra Geometry (2007) by Ron Larson.](https://reader030.fdocuments.us/reader030/viewer/2022033105/56649d885503460f94a6d1c0/html5/thumbnails/17.jpg)
Solve for the VOLUME and Surface Area:
![Page 18: SPHERES Surface Area and Volume Geometry Regular Program SY 2014-2015 Sources: Discovering Geometry (2008) by Michael Serra Geometry (2007) by Ron Larson.](https://reader030.fdocuments.us/reader030/viewer/2022033105/56649d885503460f94a6d1c0/html5/thumbnails/18.jpg)
Solve for the unknown and Surface Area:
![Page 19: SPHERES Surface Area and Volume Geometry Regular Program SY 2014-2015 Sources: Discovering Geometry (2008) by Michael Serra Geometry (2007) by Ron Larson.](https://reader030.fdocuments.us/reader030/viewer/2022033105/56649d885503460f94a6d1c0/html5/thumbnails/19.jpg)
Solve for the unknown:
![Page 20: SPHERES Surface Area and Volume Geometry Regular Program SY 2014-2015 Sources: Discovering Geometry (2008) by Michael Serra Geometry (2007) by Ron Larson.](https://reader030.fdocuments.us/reader030/viewer/2022033105/56649d885503460f94a6d1c0/html5/thumbnails/20.jpg)
Solve for the unknown:
![Page 21: SPHERES Surface Area and Volume Geometry Regular Program SY 2014-2015 Sources: Discovering Geometry (2008) by Michael Serra Geometry (2007) by Ron Larson.](https://reader030.fdocuments.us/reader030/viewer/2022033105/56649d885503460f94a6d1c0/html5/thumbnails/21.jpg)
Solve for the unknown: