Zylinder Pyramide Kegel/Der Satz von Cavalieri: Unterschied zwischen den Versionen
Main>Christine Staudermann (Die Seite wurde neu angelegt: „==Zur Person== {| |width=220px|200px |width=350px| Bonaventura Francesco Cavalieri (1598-1647) war ein italienischer Mathema…“) |
Main>Christine Staudermann |
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" 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<br><br> | <br><br> | ||
{{Lösung versteckt|1=Es kommt nicht auf die Form der Grundfläche, sondern auf den Grundflächen'''inhalt''' an!<br> | {{Lösung versteckt|1=Es kommt nicht auf die Form der Grundfläche, sondern auf den Grundflächen'''inhalt''' an!<br> |
Version vom 30. Oktober 2012, 20:42 Uhr
Zur Person
Erarbeitung des Satzes von Cavalieri
Peter: "Gib mir das rechte Glas, da passt mehr rein! Ich hab so einen Durst!" Sandra: "So ein Quatsch! In die Gläser passt doch gleich viel!" |
Zusätzliches Anschauungsmaterial zum Anfassen:
Zurück zur Ausgangsfrage:
Wer hat nun Recht? Peter oder Sandra? Begründe deine Antwort!
Du hast gerade Sachverhalte herausgearbeitet, welche Bonaventura Cavalieri in seinem berühmten (grundlegenden) Satz formuliert hat. Du kannst den Satz in deinem Schulbuch auf S. 22 nachlesen und deine Aufzeichnungen - wenn nötig - ergänzen oder berichtigen!
Es kommt nicht auf die Form der Grundfläche, sondern auf den Grundflächeninhalt an!
Übungsaufgaben
Das schiefe Prisma besitzt das gleiche Volumen wie ein senkrechtes Prisma mit den angegebenen Maßen. Also:
Der geschwungene Zylinder besitzt das gleiche Volumen wie ein senkrechter Zylinder mit den angegebenen Maßen. Also: