SPHERES Surface Area and Volume Geometry Regular Program SY 2014-2015 Sources: Discovering Geometry (2008) by Michael Serra Geometry (2007) by Ron Larson.

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Presentation transcript:

SPHERES Surface Area and Volume Geometry Regular Program SY 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? Video 1

How do we obtain the Volume of a sphere? Video 2

Volume of a Sphere Volume of a sphere with radius r

Example:

How do we obtain the Surface Area of a sphere? Video 3

How do we obtain the Surface Area of a sphere? Video 4

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 Area Volume Given a sphere with radius r

Solve for the VOLUME and Surface Area:

Solve for the unknown and Surface Area:

Solve for the unknown: