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Composite solids

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

There is no formula for a model house. You split the solid into known parts (zerlegen) or complete it to a big cuboid (ergänzen).
📄 Open worksheet (PDF, German)

The video

In the video we calculate the volume of a model house and of a solid with a missing piece.

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 Splitting
  3. 0:45 Completing
  4. 1:10 Careful, mistake!
  5. 1:35 Try it yourself

The most important points

Splitting

Add the volumes of the parts: cuboid \(6 \cdot 3 \cdot 4 = 72\,\text{cm}^3\), roof \(G = 6 \cdot 2 : 2 = 6\,\text{cm}^2\), \(V = 6 \cdot 4 = 24\,\text{cm}^3\). House: \(72 + 24 = 96\,\text{cm}^3\).

Model house made of a cuboid and a prism.
Model house made of a cuboid and a prism.
Split and add.
Split and add.

Completing

Complete to a big cuboid and subtract the missing piece: \(72 - 12 = 60\,\text{cm}^3\).

Big cuboid minus the missing piece.
Big cuboid minus the missing piece.

Careful: the triangle's area is \(6 \cdot 2 : 2 = 6\,\text{cm}^2\), not \(12\,\text{cm}^2\).

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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The worksheet – Page 4
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Show the worksheet solutions
The worksheet – Page 5
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Try it yourself

Task

A staircase made of two cuboids: bottom \(4\,\text{cm} \times 1\,\text{cm} \times 2\,\text{cm}\), top \(2\,\text{cm} \times 1\,\text{cm} \times 2\,\text{cm}\). What is the volume?

Show solution

\(8 + 4 = 12\,\text{cm}^3\).

Keep learning with a language model

Du bist meine Mathe-Lehrkraft. Ich lerne Deutsch als Zweitsprache. Unser Thema: Volumen zusammengesetzter Körper (zerlegen und addieren, ergänzen und abziehen, Quader und Prisma). 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.