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Units of volume and litres

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

How much fits in a bathtub? You measure volume in \(\text{m}^3\), \(\text{cm}^3\) or in litres. The conversion number is 1000.
📄 Open worksheet (PDF, German)

The video

In the video a cube with \(10\text{ cm}\) edge is divided into \(10 \cdot 10 \cdot 10\) small cubes.

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

Contents of the video

  1. 0:00 Introduction
  2. 0:18 The cubic decimetre
  3. 0:38 The staircase
  4. 1:00 The litre
  5. 1:17 Careful, mistake!
  6. 1:41 Try it yourself

The most important points

The cubic decimetre

\(1\text{ dm}^3 = 10 \cdot 10 \cdot 10\text{ cm}^3 = 1000\text{ cm}^3\). The length is used three times, so it is 1000.

A cube with 10\text{ cm} edge has 1\text{ dm}^3.
A cube with \(10\text{ cm}\) edge has \(1\text{ dm}^3\).

The staircase with 1000

\(\text{m}^3\) – \(\text{dm}^3\) – \(\text{cm}^3\) – \(\text{mm}^3\): from step to step \(1000 = 10^3\). More: series Körper, unit 03.

The unit staircase for volume.
The unit staircase for volume.

The litre

\(1\text{ l} = 1\text{ dm}^3\), \(1\text{ ml} = 1\text{ cm}^3\), \(1\text{ l} = 1000\text{ ml}\), \(1\text{ m}^3 = 1000\text{ l}\). Careful: \(1\text{ m}^3 = 1\,000\,000\text{ cm}^3 = 10^6\text{ cm}^3\).

Litre and millilitre.
Litre and millilitre.

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
Page 1/4
The worksheet – Page 2
Page 2/4
The worksheet – Page 3
Page 3/4
Show the worksheet solutions
The worksheet – Page 4
Page 4/4

Try it yourself

Task

a) \(2\text{ dm}^3\) to \(\text{cm}^3\) b) \(3\text{ l}\) to ml c) \(4500\text{ cm}^3\) to l

Show solution

a) \(2000\text{ cm}^3\) b) \(3000\text{ ml}\) c) \(4{,}5\text{ l}\)

Keep learning with a language model

Du bist meine Mathe-Lehrkraft. Ich lerne Deutsch als Zweitsprache. Unser Thema: Volumeneinheiten (mm³, cm³, dm³, m³, Liter, Milliliter, Umrechnungszahl 1000). 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.