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Density, Mass & Volume Relationship Demo

Density, Mass & Volume Relationship Demo
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2017-04-03 01:45
Solid GeometryGeometric Construction
This example demonstrates the fundamental physical relationship between density, mass, and volume through interactive geometry. It involves core math concepts like volume calculation, angles, ratios, set theory, difference and slope, and power functions. GeoGebra commands and objects used include OrthogonalLine, Point, Intersect, Polygon, PointIn, etc. Suitable for middle school and above students to understand basic physics formulas and mathematical modeling.

GeoGebra Commands & Parameters

  1. OrthogonalLine(A_1, xAxis) → a
  2. Point(xAxis) → B_1
  3. OrthogonalLine(B_1, xAxis) → b
  4. OrthogonalLine(C, xAxis) → c
  5. OrthogonalLine(A_1, a) → d
  6. OrthogonalLine(C, b) → e
  7. Intersect(d, yAxis) → D
  8. Intersect(xAxis, yAxis) → E
  9. Intersect(a, xAxis) → F
  10. Polygon(A_1, D, E, F) → BoxA, a_1, d_1, e_1, f
  11. Intersect(c, xAxis) → G
  12. Intersect(b, e) → H
  13. Polygon(C, G, B_1, H) → BoxB, c_1, g, b_1, h
  14. Point(Circle[I, 1]) → J
  15. Point(Circle[I_1, 1]) → J_1
  16. Point(Circle[I_2, 1]) → J_2
  17. Point(Circle[I_3, 1]) → J_3
  18. Point(Circle[I_4, 1]) → J_4
  19. Point(Circle[I_5, 1]) → J_5
  20. Point(Circle[I_6, 1]) → J_6
  21. Point(Circle[I_7, 1]) → J_7
  22. PointIn(BoxA) → M
  23. PointIn(BoxA) → N
  24. PointIn(BoxA) → O
  25. PointIn(BoxA) → P
  26. PointIn(BoxA) → Q
  27. PointIn(BoxA) → R
  28. PointIn(BoxA) → S
  29. PointIn(BoxA) → T
  30. PointIn(BoxA) → U
  31. PointIn(BoxA) → V
  32. PointIn(BoxB) → Z
  33. PointIn(BoxB) → C_1
  34. PointIn(BoxB) → D_1
  35. PointIn(BoxB) → E_1
  36. PointIn(BoxB) → F_1
  37. PointIn(BoxB) → G_1
  38. PointIn(BoxB) → H_1
  39. PointIn(BoxB) → M_1
  40. PointIn(BoxB) → N_1
  41. PointIn(BoxB) → O_1
  42. PointIn(BoxB) → P_1
  43. PointIn(BoxB) → Q_1
  44. PointIn(BoxB) → R_1
  45. PointIn(BoxB) → S_1
  46. PointIn(BoxB) → A
  47. PointIn(BoxB) → B
  48. PointIn(BoxB) → T_1
  49. PointIn(BoxB) → U_1
  50. PointIn(BoxB) → V_1
  51. PointIn(BoxB) → W_1
  52. PointIn(BoxA) → W
  53. PointIn(BoxA) → Z_1
  54. PointIn(BoxA) → A_2
  55. PointIn(BoxA) → B_2
  56. PointIn(BoxA) → C_2
  57. PointIn(BoxA) → D_2
  58. PointIn(BoxA) → E_2
  59. PointIn(BoxA) → F_2
  60. PointIn(BoxA) → G_2
  61. PointIn(BoxA) → H_2
  62. Point(Circle[I_8, 1]) → J_8
  63. Point(Circle[I_9, 1]) → J_9
  64. Point(Circle[I_{10}, 1]) → J_{10}
  65. Point(Circle[I_{11}, 1]) → J_{11}
  66. Point(Circle[I_{12}, 1]) → J_{12}
  67. Point(Circle[I_{13}, 1]) → J_{13}
  68. Point(Circle[I_{14}, 1]) → J_{14}
  69. Point(Circle[I_{15}, 1]) → J_{15}