targas-edu.de
DE ☾ A+

Surface area of the cuboid

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

How much paper do you need for a present? You unfold the cuboid and add up all faces.
📄 Open worksheet (PDF, German)

The video

In the video a cuboid is unfolded into a net. Faces of the same size get the same colour.

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

Contents of the video

  1. 0:00 Introduction
  2. 0:31 The cuboid net
  3. 0:45 Equal faces
  4. 1:14 Calculating the surface area
  5. 1:47 The formula
  6. 2:22 Careful, mistake!
  7. 2:42 Try it yourself

The most important points

All faces together are the surface area (die Oberfläche) \(O\). A cuboid net (das Quadernetz) has 6 rectangles. There are always two of the same size: bottom and top, front and back, left and right.

The cuboid net: 6 rectangles.
The cuboid net: 6 rectangles.

The surface area

Cuboid: \(O = 2 \cdot a \cdot b + 2 \cdot b \cdot c + 2 \cdot a \cdot c\). With \(a = 5\) cm, \(b = 3\) cm, \(c = 2\) cm: \(O = 30 + 12 + 20 = 62\text{ cm}^2\). Cube: \(O = 6 \cdot a \cdot a\).

Each face appears twice: 2 · 15 + 2 · 10 + 2 · 6 = 62\text{ cm}^2.
Each face appears twice: \(2 \cdot 15 + 2 \cdot 10 + 2 \cdot 6 = 62\text{ cm}^2\).
In a cube all 6 faces are equal: O = 6 · a · a.
In a cube all 6 faces are equal: \(O = 6 \cdot a \cdot a\).

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

Calculate the surface area. a) cuboid \(a = 4\) cm, \(b = 2\) cm, \(c = 1\) cm b) cube \(a = 5\) cm

Show solution

a) \(16 + 4 + 8 = 28\text{ cm}^2\) b) \(6 \cdot 25 = 150\text{ cm}^2\)

Keep learning with a language model

Du bist meine Mathe-Lehrkraft. Ich lerne Deutsch als Zweitsprache. Unser Thema: Oberfläche von Quader und Würfel (Quadernetz, O = 2 · a · b + 2 · b · c + 2 · a · c, O = 6 · a · a). 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.