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SPHERESSurface Area and Volume
Geometry Regular ProgramSY 2014-2015
Sources:
Discovering Geometry (2008) by Michael Serra
Geometry (2007) by Ron Larson
The Geometric Solids
SPHERE
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?
How do we obtain the Volume of a sphere?
https://www.youtube.com/watch?v=h4j8l3p22e8
Video 1
How do we obtain the Volume of a sphere?
https://www.youtube.com/watch?v=YNutS8eIhEs
Video 2
Volume of a Sphere
Volume of a sphere
with radius r
Example:
How do we obtain the Surface Area of a sphere?
https://www.youtube.com/watch?v=cAxHYFRx1Fs
Video 3
How do we obtain the Surface Area of a sphere?
Video 4
https://www.youtube.com/watch?v=xuPl_8o_j7k
How do we obtain the Surface Area of a sphere?
Surface Area of a Sphere
Surface Area of a sphere
with radius r
How many circle areas cover the
sphere?
Example:
Sphere
Surface AreaVolume
Given a sphere with radius r
Solve for the VOLUME and Surface Area:
Solve for the VOLUME and Surface Area:
Solve for the VOLUME and Surface Area:
Solve for the unknown and Surface Area:
Solve for the unknown:
Solve for the unknown:
Solve for the unknown: