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Volume of a Whale: Modeling with Linear Functions and Roots

Volume of a Whale: Modeling with Linear Functions and Roots
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2016-05-25 00:35
FunctionSolid GeometryIntegralSlider AnimationGraphing
This GeoGebra example demonstrates how to estimate the volume of an irregular object (a whale) using a mathematical model based on linear functions and square roots. The core concepts involve volume calculation, linear functions, root operations, and correlation between dimensions. The construction uses numerous point objects (e.g., A1 to B19) to define cross-sections of the whale's body, likely controlled by sliders or parameters, and then approximates the volume by summing volumes of cubes or prisms. This is suitable for high school or early college students to understand numerical integration, function modeling, and applying geometry to real-world problems. By adjusting parameters, learners can explore how volume changes with shape, enhancing spatial reasoning and mathematical application skills.

GeoGebra Commands & Parameters

  1. Numeric B41(6)
  2. Numeric B40(7)
  3. Numeric B43(6.408869179600884)
  4. Numeric B39(6.745898004434586)
  5. Numeric A1(-0.0015421647728783797)
  6. Numeric B1(7.45543237250554)
  7. Numeric B2(8.200443458980041)
  8. Numeric A3(0.21117021769314726)
  9. Numeric B3(8.821286031042126)
  10. Numeric A4(0.3866579332276183)
  11. Numeric A5(0.5887346965703426)
  12. Numeric B4(9.459866962305984)
  13. Numeric B5(10.080709534368069)
  14. Numeric A6(0.849307365091224)
  15. Numeric B6(10.68381374722838)
  16. Numeric A7(1.0673375571189)
  17. Numeric B7(11.127272727272725)
  18. Numeric A8(1.4289486073111435)
  19. Numeric B8(11.411086474501106)
  20. Numeric A9(1.7320637523252298)
  21. Numeric B9(11.109534368070952)
  22. Numeric A10(1.950093944352906)
  23. Numeric B10(10.719290465631927)
  24. Numeric A11(2.215984422435438)
  25. Numeric B11(10.222616407982258)
  26. Numeric A12(2.391472137969909)
  27. Numeric B12(9.708203991130818)
  28. Numeric B13(9.193791574279377)
  29. Numeric A14(2.8541215698335143)
  30. Numeric B14(8.679379157427935)
  31. Numeric A15(3.205097000902456)
  32. Numeric B15(7.881152993348112)
  33. Numeric A16(3.077469571422841)
  34. Numeric B16(8.235920177383589)
  35. Numeric A17(3.428445002491783)
  36. Numeric B17(7.490909090909088)
  37. Numeric A18(3.7528313857524718)
  38. Numeric B18(7.082926829268289)
  39. Numeric A19(4)
  40. Numeric B19(7)
  41. Numeric A20(4.231434246301034)
  42. Numeric B20(7.0119733924611936)
  43. Numeric A21(4.460100057452011)
  44. Numeric B21(7.278048780487802)
  45. Numeric B22(7.810199556541017)
  46. Numeric A23(4.486689105260265)
  47. Numeric B23(8.572949002217293)
  48. Numeric A24(4.428193200082108)
  49. Numeric B24(9.229268292682924)
  50. Numeric A25(4.4122397713971555)
  51. Numeric B25(9.867849223946783)
  52. Numeric A26(4.460100057452011)
  53. Numeric B26(10.524168514412414)
  54. Numeric A27(4.890842631945714)
  55. Numeric B27(10.25809)
  56. Numeric A28(4.768533012027748)
  57. Numeric B28(10.666075388026604)
  58. Numeric A29(4.582409677369976)
  59. Numeric B29(11.091796008869176)
  60. Numeric B30(10)