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The cylinder

This page was translated from German with AI. It has not been checked by a native speaker. Original page in German

A cylinder is like a prism with a circle as its base. Its lateral surface is a rectangle – like with a paint roller.
📄 Open worksheet (PDF, German)

The video

In the video a cylinder rolls one turn across the table. The lateral surface paints a rectangle.

Subtitles are available in ten languages. Choose them at the bottom right of the video.

Contents of the video

  1. 0:00 Introduction
  2. 0:14 The cylinder
  3. 0:42 The volume
  4. 1:26 The lateral surface
  5. 2:05 The surface area
  6. 2:40 Careful, mistake!
  7. 2:58 Try it yourself

The most important points

The volume

Base: \(G = \pi \cdot r^2\). Volume: \(V = G \cdot h = \pi \cdot r^2 \cdot h\). With \(r = 1{,}5\) cm and \(h = 4\) cm: \(V \approx 7{,}07 \cdot 4 \approx 28{,}3\text{ cm}^3\).

V = \pi · r^2 · h.
\(V = \pi \cdot r^2 \cdot h\).

Lateral surface and surface area

The lateral surface (der Mantel) is a rectangle: \(u = 2 \cdot \pi \cdot r\) long, \(h\) wide. \(M = 2 \cdot \pi \cdot r \cdot h\). \(O = 2 \cdot \pi \cdot r^2 + 2 \cdot \pi \cdot r \cdot h\).

One turn: u \approx 9{,}42 cm, M \approx 37{,}7\text{ cm}^2.
One turn: \(u \approx 9{,}42\) cm, \(M \approx 37{,}7\text{ cm}^2\).

Careful: the formulas use the radius \(r\), not the diameter.

The net: a rectangle and two circles. O \approx 51{,}8\text{ cm}^2.
The net: a rectangle and two circles. \(O \approx 51{,}8\text{ cm}^2\).

The worksheet

Here you can see the worksheet for the video (in German). First it explains everything again, then there are practice tasks at three levels. You can also open it as a PDF and print it.

📄 Open worksheet (PDF, German)

The worksheet – Page 1
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The worksheet – Page 2
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The worksheet – Page 3
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Show the worksheet solutions
The worksheet – Page 4
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Try it yourself

Task

Use \(\pi \approx 3{,}14\). A cylinder has \(r = 3\) cm and \(h = 10\) cm. a) volume b) lateral surface

Show solution

a) \(282{,}6\text{ cm}^3\) b) \(188{,}4\text{ cm}^2\)

Keep learning with a language model

Du bist meine Mathe-Lehrkraft. Ich lerne Deutsch als Zweitsprache. Unser Thema: Zylinder (V = π · r² · h, Mantel M = 2 · π · r · h, Oberfläche). Stelle mir nacheinander fünf kurze Aufgaben. Warte immer auf meine Antwort. Sag mir dann, ob sie richtig ist, und erkläre kurz, warum. Benutze einfache deutsche Sätze.

How this was made: The idea, structure and examples of the series are mine. I made them with the help of AI: a language model (LLM) built the slides of the video following my instructions. The voice was generated with Qwen3-TTS, modelled on my own voice.

The subtitles, the translations, the worksheet and this page were also made with the help of AI. The translations have not been checked by native speakers.

The videos, worksheets, texts and prompts in this series are licensed under CC BY 4.0: you may use, change and share them if you name the source.