Schachteln aus einem Din-A4-Blatt - Bastelstunde

Aus einem normalen Din-A4-Blatt kannst du in Windeseile eine Schachtel basteln, indem du in die vier Ecken gleich große Quadrate einzeichnest, diese an einer Seite einschneidest und umklappst und sie dann an die Seite der Schachtel anklebst.
Zeichne in Din-A4-Blätter Quadrate mit den Seiten Längen 2cm, 4 cm, 6 cm, 8 cm und 10 cm.[br]Erstellt daraus Schachteln und vergleicht deren Größe.
So könnten vier der Schachteln aussehen:
Vier Schachteln
Um ein Gefühl dafür zu bekommen, wie groß die verschiedenen Schachteln sind, könnt ihr sie befüllen - z.B. mit Reis, mit Kugeln aus zerknülltem Altpapier oder mit Smarties. Beschreibe möglichst genau, wie sich die Grüße der Schachteln verändert, wenn die Eckenquadrate um jeweils 2 cm größer werden.
In welche Schachtel passen wie viele Smarties?
Für welche Seitenlänge der Quadrate in den Ecken wird die Schachtel am größten?

Pyramide aus einem Din-A4-Blatt

Aufgabe 1
Wenn du auf ein Din-A4-Blatt (210mm x 297mm) mittig ein Quadrat einzeichnest und auf jede Quadratseite ein möglichst großes gleichschenkliges Dreieck aufsetzt, erhäslt du das Netz einer Pyramide mit quadratischer Grundfläche.
Erstelle zwei solcher Pyramiden und ermittle jeweils das Volumen. Vergleiche!
Aufgabe 2
Nimm dir ein Din-A4-Blatt und versuche, die größtmögliche Pyramide zu basteln.
Übersichtlich: Auch ohne Rechnung ist klar, dass die Pyramiden nicht übermäßig viel Inhalt fassen.
Aufgabe 3
Mit dem folgenden Applet kannst du mit Hilfe des Schiebereglers die größtmögliche Pyramide finden.[br]Vergleiche mit deinem Bastelergebnis.
Markiere alle Aussagen, die ohne Wenn und Aber korrekt sind:[br]Wenn die Grundfläche vergrößert wird, dann...
Aufgabe 4
Begründe, dass die Funktion [math]v[/math] mit [math]v(t)=\frac{1}{3}\cdot\left(2t\right)^2\cdot\sqrt{\left(10,5-t\right)^2-t^2}[/math] das Pyramidenvolumen in Abhängigkeit von [math]t[/math] angibt. [br]Bestimme den den "optimalen" Wert von t rechnerisch. (Statt mit [math]t[/math] rechnen wir hier mit [math]x[/math].)

Kegel aus einem Din-A4-Blatt

Aufgabe 1
Wenn du mit einem Zirkel genau in die Mitte eines Din-A4-Blattes einstichst, kannst du einen Kreis mit dem Radius [math]r=10,5cm[/math] einzeichnen.[br]Wenn du nun zwei Punkte auf dem Kreis wählst, diese mit dem Mittelpunkt verbindest und den zugehörigen Kreissektor herausschneidest (bzw. als Klebelasche verwendest), kannst du einen Kegel basteln.
Erstelle zwei solcher Kegel und ermittle jeweils das Volumen. Vergleiche!
Aufgabe 2
Nimm dir ein Din-A4-Blatt und versuche, den größtmöglichen Kegel zu basteln.
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[/img][br]Wie sollte α gewählt werden, damit das Volumen des Kegel möglichst groß ist?
Aufgabe 3
Mit dem folgenden Applet kannst du mit Hilfe des Schiebereglers den größtmöglichen Kegel finden.[br]Vergleiche mit deinem Bastelergebnis.
Markiere alle Aussagen, die ohne Wenn und Aber korrekt sind:[br]Wenn der Winkel α vergrößert wird, dann...
Begründe deine Einschätzung der letzten Aussage:[br]"Wenn der Winkel α vergrößert wird, dann vergrößert sich das Volumen des Kegels."

Alles ist möglich!

Bislang wurden dir in den Aktivitäten Vorgaben über die Form gemacht, die du aus einem Din-A4-Blatt erstellen solltest. Nun sind deiner Kreativität keine Grenzen gesetzt.[br]Erstelle ein Gefäß deiner Wahl aus einem Din-A4-Blatt, und zwar so, dass möglichst viel hineinpasst.
Deiner Phantasie sind keine Grenzen gesetzt!
Festlegen auf eine Form
Welche Form soll dein Gefäß haben?[br]Beschreibe es mit Hilfe von mathematischen Fachbegriffen.
Volumen bestimmen
Berechne für dein Gefäß das Volumen, das es fassen kann.
Vergleiche das Fassungsvermögen deines Gefäßes mit dem der quaderförmigen Schachtel, der Tüte und der Pyramide.

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