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Volume Calculation of Composite Solids

Volume Calculation of Composite Solids
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2023-03-21 21:14
Solid GeometryGeometric ConstructionSlider Animation
In collections Ⓔ Volumen zusammengesetzter Körper aus Quader und Würfel
This example demonstrates using GeoGebra to decompose composite geometric solids and calculate their volumes. Key mathematical concepts include volume formulas for solids, decomposition into unit cubes, and volume calculation of rectangular prisms. Construction involves GeoGebra commands like Textfield, Sum, Segment, and parameter input. Suitable for middle and high school students for geometry learning and practical application.

GeoGebra Commands & Parameters

  1. Textfield(input1) → InputBox1
  2. Textfield(input2) → InputBox2
  3. Sum({attemptCountInputBox1, attemptCountInputBox2, attemptCountInputBox3, attemptCountInputBox4, attemptCountInputBox5}) → attemptCount
  4. Shuffle(Sequence[Random[0, 10], i, 1, 100]) → randomNosForX, {7, 3, 10, 7, 4, 4, 6, 8, 5, 5, 2, 3, 3, 3, 4, 4, 9, 1, 0, 8, 6, 4, 8, 6, 7, 0, 7, 9, 1, 5, 8, 8, 3, 4, 7, 2, 0, 9, 4, 1, 9, 0, 10, 0, 6, 3, 6, 0, 0, 8, 10, 0, 4, 8, 5, 9, 6, 10, 2, 0, 3, 1, 1, 0, 2, 2, 4, 9, 5, 0, 7, 2, 3, 1, 7, 4, 0, 2, 2, 3, 2, 5, 9, 6, 5, 8, 6, 9, 0, 1, 10, 0, 5, 10, 4, 6, 5, 5, 10, 8}
  5. Element(randomNosForX, Mod[questionCount, 100] + 1) → numX
  6. U(A, pointVec) → l1, l2, C, D, E, F, G, H, l0BG1, l4Kontur, l2Mantel, l4lines, l4linesManual, l5FG1, l5FG2, B
  7. LaTeX(step, true, true) → Text1
  8. Segment(pointOption1, F) → segmentOption1
  9. Segment(F, pointOption2) → segmentOption2
  10. Segment(E, pointOption3) → segmentOption3
  11. Segment(E, pointOption4) → segmentOption4
  12. Translate(C, pointVec) → C'
  13. Translate(pointOption4, pointVec) → pointOption4'
  14. Translate(F, pointVec) → F'
  15. Translate(G, pointVec) → G'
  16. Translate(H, pointVec) → H'
  17. If(option1, A, pointOption1) → pointObject11
  18. If(option1, pointOption2, F) → pointObject12
  19. Translate(D, pointVec) → D'
  20. Segment(pointOption4, pointOption4') → segmentOption41
  21. Translate(B, pointVec) → B'
  22. If(¬option4, pointOption4', B') → pointObject31
  23. If(¬option4, pointOption4, B) → pointObject32
  24. If(¬option4, E, pointOption3) → pointObject33
  25. If(option2 ∧ option4, 1, option1 ∧ option4, 2, option1 ∧ option3, 3, 4) → typ
  26. Segment(G', D') → segmentFilled1
  27. Segment(G, D) → segmentFilled2
  28. Segment(pointOption1, F) → segmentCutted1
  29. Segment(E, pointOption4) → segmentCutted2
  30. Segment(pointOption4, pointOption4') → segmentCutted3
  31. Segment(B', C') → f
  32. Segment(C', D') → g
  33. Segment(D', D) → h
  34. Segment(E', F') → i
  35. Segment(F', G') → j
  36. Segment(G', H') → k
  37. Segment(H', H) → l
  38. If(step ∈ {4, 5}, (-23.75, 32.5), (-23.75, 35)) → speechbubble12
  39. If(step ∈ {4, 5}, (0, 32.5), (3.75, 35)) → speechbubble13
  40. If(step ∈ {4, 5}, (0, 40.3), (3.75, 39.5)) → speechbubble14
  41. If(step ∈ {4, 5}, (-23.75, 40.3), (-23.75, 39.5)) → speechbubble15
  42. Textfield(input3) → InputBox3
  43. Textfield(input4) → InputBox4
  44. Textfield(input71) → InputBox71
  45. Textfield(input72) → InputBox72
  46. Textfield(input73) → InputBox73
  47. Textfield(input74) → InputBox74
  48. Textfield(input75) → InputBox75
  49. If((¬option1) ∧ (¬option2), input72 ≟ ((3 * 5) * 2), true) → correct72
  50. If((¬option3) ∧ (¬option4), input74 ≟ ((3 * 5) * 2), true) → correct74
  51. Dilate(Translate[l5FG2, (-10, 0)], step6Scalefactor, CenterOfDilation) → l3
  52. Dilate(Translate[listObject1, translationVector], step6Scalefactor, CenterOfDilation) → listObject1'
  53. Dilate(Translate[listObjectFilledLeftBottom, translationVector], step6Scalefactor, CenterOfDilation) → listObjectFilledLeftBottom'
  54. Dilate(Translate[listObjectFilledRightBottom, translationVector], step6Scalefactor, CenterOfDilation) → listObjectFilledRightBottom'
  55. Dilate(Segment[Translate[F, translationVector], Translate[pointOption2, translationVector]], step6Scalefactor, CenterOfDilation) → segmentOption2'
  56. Dilate(Segment[Translate[E, translationVector], Translate[pointOption3, translationVector]], step6Scalefactor, CenterOfDilation) → segmentOption3'
  57. Dilate(Segment[Translate[pointOption1, translationVector], Translate[F, translationVector]], step6Scalefactor, CenterOfDilation) → segmentOption1'
  58. Dilate(Translate[listObject3, translationVector], step6Scalefactor, CenterOfDilation) → listObject3'
  59. Dilate(Translate[listObject2, translationVector], step6Scalefactor, CenterOfDilation) → listObject2'
  60. Dilate(Translate[l0BG1, translationVector], step6Scalefactor, CenterOfDilation) → step6l0BG1'
  61. Dilate(Translate[l2Mantel, translationVector], step6Scalefactor, CenterOfDilation) → step6l2Mantel'
  62. Dilate(Translate[l4Kontur, translationVector], step6Scalefactor, CenterOfDilation) → step6l4Kontur'
  63. Dilate(Translate[l4linesManual, translationVector], step6Scalefactor, CenterOfDilation) → step6l4linesManual'
  64. Dilate(Translate[l5FG1, translationVector], step6Scalefactor, CenterOfDilation) → step6l5FG1'
  65. Dilate(Translate[l5FG2, translationVector], step6Scalefactor, CenterOfDilation) → step6l5FG2'
  66. Dilate(Segment[Translate[pointOption4, translationVector], Translate[pointOption4', translationVector]], step6Scalefactor, CenterOfDilation) → segmentOption41'
  67. Dilate(Translate[listObjectFilledRightBottom, translationVector], step6Scalefactor, CenterOfDilation) → listObjectFilledRightBottomBG'
  68. PolyLine(Dilate[B, step6Scalefactor, CenterOfDilation], Dilate[B', step6Scalefactor, CenterOfDilation], Dilate[A, step6Scalefactor, CenterOfDilation], Dilate[C', step6Scalefactor, CenterOfDilation], Dilate[D', step6Scalefactor, CenterOfDilation], Dilate[D, step6Scalefactor, CenterOfDilation], Dilate[E', step6Scalefactor, CenterOfDilation], Dilate[F', step6Scalefactor, CenterOfDilation], Dilate[G', step6Scalefactor, CenterOfDilation], Dilate[H', step6Scalefactor, CenterOfDilation], Dilate[H, step6Scalefactor, CenterOfDilation]) → m
  69. PolyLine(Translate[E, translationVector], Translate[pointOption4, translationVector], Translate[I', translationVector]) → n
  70. Dilate(PolyLine[Translate[E, translationVector], Translate[pointOption4, translationVector], Translate[I', translationVector]], step6Scalefactor, CenterOfDilation) → segmentOption4'
  71. Translate(cora, (7, 0)) → cora'
  72. Textfield(input31) → InputBox31
  73. Textfield(input32) → InputBox32
  74. Translate(elia, (30.434007263501044, -17.511741828561323)) → elia'
  75. Translate(Mirror[speechbubble2, x = -18], (0.5, -20)) → speechbubble3
  76. Textfield(input2a) → InputBox2a
  77. Textfield(input3a) → InputBox3a
  78. Textfield(input1a) → InputBox1a
  79. Textfield(input1b) → InputBox1b

AI Drawing Prompt Reference

In a 3D coordinate view, draw a composite solid made from two matching rectangular prisms, arranged so it can be decomposed for a volume calculation. Include on-screen step text and input-box style parameter prompts to guide the process. Construct a base set of points and a central edge, then generate the top/bottom and left/right parts by translating the corresponding points. Connect the boundary using several line segments to form the outer contour (before cutting), and use translated corresponding edges to create the cut/inner boundary lines. Keep both the cut-edged segments and the filled contour edges visible, together with the explanatory step text for the calculation.
The prompt above was compiled from the original drawing commands and is for reference only.