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Maximum Volume of a Box

Maximum Volume of a Box
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2019-04-02 19:24
Coordinate GeometryCalculusOptimization
This example demonstrates how to construct a box with maximum volume from a given rectangular sheet of paper by cutting out equal squares from each corner. It involves core math concepts like functions, calculus optimization, and coordinate geometry. Key GeoGebra commands used include Intersect, Textfield, Segment, and Max. Suitable for high school mathematics education, particularly for teaching applications of calculus and optimization problem-solving.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → A
  2. Textfield(w) → inputBox1
  3. Textfield(h) → Height_1
  4. Intersect(y = y(C_2), x = x(C_1)) → C_3
  5. Intersect(y = y(D_2), x = x(D_1)) → D_3
  6. Intersect(y = y(B_2), x = x(B_1)) → B_3
  7. Intersect(y = y(A_2), x = x(A_1)) → A_3
  8. Segment(D_1, C_1) → a
  9. Segment(C_3, C_2) → d
  10. Segment(C_2, A_2) → e
  11. Segment(A_3, A_2) → f
  12. Segment(A_1, B_1) → i
  13. Segment(B_2, B_3) → k
  14. Segment(D_2, B_2) → l
  15. Segment(D_2, D_3) → m
  16. Segment(D, D_1) → p
  17. Segment(D, D_2) → q
  18. Segment(B_2, B) → r
  19. Segment(B, B_1) → s
  20. Segment(A_1, A) → t
  21. Segment(A_2, A) → a_1
  22. Segment(C_2, C) → b_1
  23. Segment(C, C_1) → c_1
  24. Segment(B_3, D_1) → j
  25. Segment(D_3, B_1) → n
  26. Segment(C_3, A_1) → b
  27. Segment(A_3, C_1) → g
  28. Segment(B_3, D_3) → d_1
  29. Segment(D_3, C_3) → e_1
  30. Segment(B_3, A_3) → f_1
  31. Segment(A_3, C_3) → g_1
  32. Max(h_1, 0, (0.5 * Max[h, w])) → y_m