Der Satz von Cavalieri: Unterschied zwischen den Versionen

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(Die Seite wurde neu angelegt: „==Zur Person== {| |width=220px|200px |width=350px| Bonaventura Francesco Cavalieri (1598-1647) war ein italienischer Mathema…“)
 
(Erarbeitung des Satzes von Cavalieri)
Zeile 63: Zeile 63:
 
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" showResetIcon = "false" enableRightClick = "false" errorDialogsActive = "true" enableLabelDrags = "false" showMenuBar = "false" showToolBar = "false" showToolBarHelp = "false" showAlgebraInput = "false" useBrowserForJS = "true" allowRescaling = "false" />
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" 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{{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, 22:42 Uhr

Zur Person

Bonaventura Cavalieri.jpeg Bonaventura Francesco Cavalieri (1598-1647) war ein italienischer Mathematiker und Astronom.

Im "Satz von Cavalieri" (auch "Prinzip von Cavalieri" genannt) geht es um die Volumengleichheit zweier Körper.


Erarbeitung des Satzes von Cavalieri


Zylinder gerade geschwungen.jpg

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!"



Vorlage:Arbeiten

Zusätzliches Anschauungsmaterial zum Anfassen:
Wenn es dir schwer fällt, dir das Ganze richtig vorzustellen, nimm dir vorne am Pult zwei der Bierdeckelstapel und stelle die einzelnen Situationen damit nach.








Zurück zur Ausgangsfrage:

Wer hat nun Recht? Peter oder Sandra? Begründe deine Antwort!



Vorlage:Arbeiten
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!



Vorlage:Arbeiten



Es kommt nicht auf die Form der Grundfläche, sondern auf den Grundflächeninhalt an!

Bsp.: Ein Prisma mit quadratischer Grundflächen und ein Prisma mit dreieckiger Grundfläche haben das gleiche Volumen, wenn ihre Grundflächeninhalte, ihre Höhe und die zur Grundfläche parallelen Schnittflächen in gleicher Höhe gleich groß sind.




Übungsaufgaben

Vorlage:Arbeiten

Das schiefe Prisma besitzt das gleiche Volumen wie ein senkrechtes Prisma mit den angegebenen Maßen. Also: V=27000cm^{3}=27dm^{3}
Der geschwungene Zylinder besitzt das gleiche Volumen wie ein senkrechter Zylinder mit den angegebenen Maßen. Also: V\approx 1696,46cm^{3}\approx 1,7dm^{3}

Zu deiner Lösung gehört auch der Rechenweg!



Vorlage:Arbeiten