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Pyramid, cone and sphere

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

With an experiment with water you find the volume of the pyramid, the cone and the sphere.
📄 Open worksheet (PDF, German)

The video

In the video water is poured: from the pyramid into the cuboid, from the cone and the sphere into a cylinder.

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

Contents of the video

  1. 0:00 Introduction
  2. 0:19 The pyramid
  3. 1:15 The cone
  4. 1:50 The sphere
  5. 2:38 Careful, mistake!
  6. 2:58 Try it yourself

The most important points

Pyramid and cone

Pour three times, then the cuboid is full. Pyramid (die Pyramide): \(V = \frac{1}{3} \cdot G \cdot h\). Cone (der Kegel): \(V = \frac{1}{3} \cdot \pi \cdot r^2 \cdot h\).

3 pyramids fill one cuboid: V = 36 : 3 = 12\text{ cm}^3.
3 pyramids fill one cuboid: \(V = 36 : 3 = 12\text{ cm}^3\).
3 cones fill one cylinder.
3 cones fill one cylinder.

The sphere

The sphere (die Kugel) fills a cylinder with \(h = 2 \cdot r\) to two thirds. Sphere: \(V = \frac{4}{3} \cdot \pi \cdot r^3\).

The sphere fills the cylinder to 2/3.
The sphere fills the cylinder to \(\frac{2}{3}\).

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
Page 3/4
Show the worksheet solutions
The worksheet – Page 4
Page 4/4

Try it yourself

Task

Use \(\pi \approx 3{,}14\). a) pyramid: \(G = 12\text{ cm}^2\), \(h = 5\) cm b) cone: \(r = 3\) cm, \(h = 10\) cm c) sphere: \(r = 3\) cm

Show solution

a) \(20\text{ cm}^3\) b) \(94{,}2\text{ cm}^3\) c) \(113{,}04\text{ cm}^3\)

Keep learning with a language model

Du bist meine Mathe-Lehrkraft. Ich lerne Deutsch als Zweitsprache. Unser Thema: Volumen von Pyramide, Kegel und Kugel (V = 1/3 · G · h, V = 1/3 · π · r² · h, V = 4/3 · π · r³). 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.