SPHERES Surface Area and Volume

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Presentation transcript:

SPHERES Surface Area and Volume Geometry Regular Program SY 2015-2016 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 a plane cuts a sphere along the center, then the plane contains the great circle. If you were to slice a pingpong ball, where do you slice it to get the largest circular cross-section? Is the equator In a globe a great circle?

Volume of a sphere with radius r

Example:

Surface Area of a Sphere Surface Area of a sphere with radius r How many circle areas cover the sphere?

Example:

Given a sphere with radius r Volume Surface Area

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: