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Density

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

Wood and iron are the same size, but iron is much heavier. The density (die Dichte) tells you how much mass is in \(1\text{ cm}^3\).
📄 Open worksheet (PDF, German)

The video

In the video wood floats, ice floats just barely, and iron sinks.

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

Contents of the video

  1. 0:00 Introduction
  2. 0:15 Density
  3. 0:48 Calculating mass
  4. 1:08 Float or sink
  5. 1:30 Careful, mistake!
  6. 1:43 Try it yourself

The most important points

Density

density = mass : volume, \(\rho = m : V\). Iron: \(790\text{ g} : 100\text{ cm}^3 = 7{,}9\text{ g/cm}^3\). Wood: \(0{,}7\text{ g/cm}^3\). Water: \(1\text{ g/cm}^3\).

Density of iron, wood and water.
Density of iron, wood and water.

Calculating mass

\(m = \rho \cdot V\). Aluminium (\(2{,}7\text{ g/cm}^3\)), \(50\text{ cm}^3\): \(m = 2{,}7 \cdot 50 = 135\text{ g}\).

Mass = density times volume.
Mass = density times volume.

Float or sink

Density smaller than 1: the body floats in water. Density greater than 1: it sinks. Careful: density is mass divided by volume, not volume divided by mass.

Wood floats, ice floats just barely, iron sinks.
Wood floats, ice floats just barely, iron sinks.

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
Page 4/4

Try it yourself

Task

a) Copper: \(20\text{ cm}^3\), \(178\text{ g}\). What is the density? b) Gold has \(19{,}3\text{ g/cm}^3\). How heavy are \(10\text{ cm}^3\)?

Show solution

a) \(178 : 20 = 8{,}9\text{ g/cm}^3\) b) \(19{,}3 \cdot 10 = 193\text{ g}\)

Keep learning with a language model

Du bist meine Mathe-Lehrkraft. Ich lerne Deutsch als Zweitsprache. Unser Thema: Dichte (Masse durch Volumen, g/cm³, Masse berechnen, schwimmen und sinken). 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.