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Home » The radius of the sphere is 5 centimeters. - Ready Digital AB

The radius of the sphere is 5 centimeters. - Ready Digital AB

📅 March 7, 2026 👤 scraface

Mar 07, 2026

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📌 Gegeben ist ein rechtwinkliges Dreieck mit Hypotenuse \(c = 13\) cm und einer Kathete \(a = 5\) cm. Zuerst die andere Kathete \(b\) mit dem Satz des Pythagoras finden:

📌 b = \sqrt{c^2 - a^2} = \sqrt{13^2 - 5^2} = \sqrt{169 - 25} = \sqrt{144} = 12 \text{ cm}.

📌 Der Radius \(r\) des eingeschriebenen Kreises in einem rechtwinkligen Dreieck ist gegeben durch:

📌 r = \frac{a + b - c}{2} = \frac{5 + 12 - 13}{2} = \frac{4}{2} = 2 \text{ cm}.

📌 Somit beträgt der Radius des eingeschriebenen Kreises \(\boxed{2}\) cm.

📌 Frage: Ein regelmäßiges Sechseck ist in einen Kreis mit Radius 6 cm eingeschrieben. Wie ist der Umfang des Sechsecks in Zentimetern?

📌 Ein regelmäßiges Sechseck, das in einen Kreis eingeschrieben ist, hat jede Seitenlänge gleich dem Radius des Kreises. Da der Radius 6 cm beträgt, ist jede Seite des Sechsecks 6 cm lang. Ein regelmäßiges Sechseck hat 6 Seiten, also ist sein Umfang:

📌 \times 6 = 36 \text{ cm}.

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