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Archimedes' Hat Box Theorem

A unit sphere is placed in a unit cylinder. You can cut off parts of the two surfaces with planes perpendicular to the axis of the cylinder. The lateral surface area of the partial cylinder equals that of the spherical segment.

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 Sándor Kabai
"Archimedes' Hat Box Theorem"
 http://demonstrations.wolfram.com/ArchimedesHatBoxTheorem/
 Wolfram Demonstrations Project
 Published: October 15, 2008
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US Common Core State Standards, Mathematics
 
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