Mit der Formel U=2π⋅r zur Berechung des Umfangs U eines Kreises mit dem Radius r können wir eine Formel für seinen Flächeninhalt herleiten. Dazu zerlegen wir den Kreis zunächst in n gleiche Teile und ordnen sie zu einem Rechteck an.
Tauscht euch aus! Wie entsteht aus den einzelnen Teilstücken des Kreises annähernd das Rechteck?
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[/img]
1) Wie lässt sich der Flächeninhalt mit dem Durchmesser d berechnen? [br]2) Mit welchem Faktor x muss man den Radius vergrößern, damit sich der Flächeninhalt verdoppelt?