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Calculating and Explaining Cuboid Volume with V = a·b·c

Calculating and Explaining Cuboid Volume with V = a·b·c
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2023-03-23 22:45
In collections Quader und Würfel - Volumen Wiederholung: Quader und Würfel
This GeoGebra example uses cuboid and cube scenarios to demonstrate how to compute volume via V = a·b·c, and it includes open questions that ask learners to explain why a particular calculation works, identify mistakes, and solve for an unknown edge length. The key math concepts are solid geometry volume, the meaning of volume as counting unit cubes, applying and justifying the cuboid volume formu

GeoGebra Commands & Parameters

  1. Textfield(vol) → InputBox4
  2. Shuffle(Sequence[Random[3, 7], i, 1, 100]) → randomNosFork, {4, 5, 4, 4, 3, 4, 3, 7, 3, 6, 7, 6, 5, 7, 6, 4, 4, 4, 5, 7, 4, 4, 7, 5, 5, 3, 4, 3, 4, 7, 6, 3, 3, 6, 5, 5, 4, 3, 6, 6, 6, 4, 4, 3, 3, 4, 6, 7, 5, 3, 7, 3, 4, 7, 4, 3, 6, 5, 6, 6, 3, 7, 6, 5, 5, 7, 5, 6, 5, 7, 5, 3, 7, 5, 4, 4, 4, 4, 6, 5, 5, 3, 6, 7, 3, 4, 3, 7, 3, 3, 4, 7, 4, 5, 4, 3, 4, 7, 3, 6}
  3. Element(randomNosFork, Mod[questionCount, 100] + 1) → k
  4. Shuffle(Sequence[Random[1, 7], i, 1, 100]) → randomNosForB, {7, 1, 6, 2, 2, 1, 1, 2, 3, 6, 3, 6, 3, 5, 7, 5, 1, 4, 4, 3, 1, 3, 7, 1, 7, 2, 7, 1, 4, 5, 5, 1, 5, 4, 2, 7, 6, 1, 6, 6, 7, 6, 6, 4, 4, 3, 6, 7, 6, 1, 6, 2, 3, 6, 5, 7, 5, 4, 5, 2, 2, 6, 7, 1, 7, 4, 6, 3, 4, 4, 5, 3, 6, 5, 4, 4, 3, 2, 5, 2, 6, 6, 7, 6, 3, 4, 3, 5, 1, 1, 3, 4, 1, 4, 5, 7, 6, 3, 5, 3}
  5. Shuffle(Sequence[Random[10, 59], i, 1, 100]) → randomNosForA, {20, 23, 51, 21, 23, 43, 13, 40, 31, 14, 28, 52, 40, 41, 39, 45, 41, 51, 23, 46, 56, 12, 10, 28, 25, 37, 12, 27, 57, 50, 25, 11, 17, 52, 59, 43, 17, 20, 33, 44, 43, 35, 34, 25, 45, 49, 21, 24, 50, 34, 57, 37, 48, 32, 56, 11, 42, 20, 14, 35, 37, 53, 43, 19, 47, 49, 35, 14, 53, 15, 31, 46, 56, 34, 43, 23, 38, 55, 21, 55, 47, 40, 58, 31, 58, 28, 15, 30, 23, 48, 31, 23, 30, 26, 13, 36, 29, 59, 21, 18}
  6. Element(randomNosForA, Mod[questionCount, 100] + 1) → a
  7. Shuffle(Sequence[Random[6, 9], i, 1, 100]) → randomNosForC, {7, 8, 6, 8, 7, 7, 6, 9, 9, 9, 8, 6, 8, 8, 8, 6, 9, 6, 8, 8, 8, 7, 9, 6, 6, 7, 6, 8, 7, 9, 9, 8, 8, 6, 6, 6, 6, 9, 9, 6, 8, 8, 7, 8, 8, 7, 6, 6, 6, 9, 6, 7, 9, 7, 7, 6, 7, 8, 8, 9, 9, 8, 7, 6, 9, 8, 8, 6, 9, 9, 6, 7, 7, 9, 7, 6, 9, 9, 7, 7, 7, 7, 7, 9, 6, 7, 9, 6, 6, 7, 8, 7, 8, 8, 8, 9, 6, 6, 9, 9}
  8. Element(randomNosForC, Mod[questionCount, 100] + 1) → c
  9. Max(groessen) → maxNum
  10. Shuffle(Sequence[Random[1, 4], i, 1, 100]) → randomNosForEinheit, {1, 2, 2, 2, 1, 4, 1, 3, 3, 4, 2, 3, 4, 4, 1, 2, 2, 2, 4, 1, 1, 1, 2, 4, 3, 1, 2, 3, 4, 4, 4, 4, 2, 3, 1, 2, 2, 2, 4, 2, 2, 2, 2, 1, 3, 1, 2, 4, 3, 1, 4, 2, 3, 3, 1, 3, 4, 1, 4, 3, 3, 3, 3, 4, 1, 2, 1, 4, 2, 1, 1, 1, 4, 3, 4, 1, 2, 1, 2, 3, 4, 4, 2, 3, 1, 1, 3, 2, 1, 1, 3, 1, 1, 2, 1, 3, 3, 1, 2, 3}
  11. Element(randomNosForEinheit, Mod[questionCount, 100] + 1) → Einheit
  12. If(maxNum > 20, 0.03, 0.1) → kuerzung
  13. Rotate(B + (((b * kuerzung) * verzerrung), 0), winkel, B) → C
  14. Rotate(A + (((b * kuerzung) * verzerrung), 0), winkel, A) → D
  15. Rotate(F + (((b * kuerzung) * verzerrung), 0), winkel, F) → G
  16. Rotate(E + (((b * kuerzung) * verzerrung), 0), winkel, E) → H
  17. Segment(A, B) → ab
  18. Segment(B, C) → bc
  19. Segment(C, D) → cd
  20. Segment(A, E) → ae
  21. Segment(B, F) → bf
  22. Segment(E, F) → ef
  23. Segment(E, H) → eh
  24. Segment(F, G) → fg
  25. Segment(G, H) → gh
  26. Segment(A, D) → ad
  27. Segment(D, H) → dh
  28. Segment(C, G) → cg
  29. SpeechBubbleRight(Bubble + (0.47, -0.1), 10.7, 1.3) → bubble2
  30. Textfield(aInput) → InputBox1
  31. Textfield(bInput) → InputBox2
  32. Textfield(cInput) → InputBox3
  33. SelectedIndex(selectedDrop) → index
  34. SpeechBubbleRight(PBubble4, 4.6, 1.7) → bubble3
  35. SpeechBubbleRight(Bubble1, 8, 1.5) → poly1
  36. SpeechBubbleRight(PBubble3, 8, 2.5) → poly2