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Volume of Planter Box

Volume of Planter Box
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2016-09-09 12:37
FunctionSolid GeometryDerivativeGeometric ConstructionSlider Animation
This example demonstrates how to calculate the volume of a planter box by rotating a 2D shape. It involves core math concepts like volume calculation, rotational geometry, functions, and derivatives. GeoGebra commands and objects used include Function, Segment, Rotate, Line, Intersect, Angle, Polygon, Derivative, Root, and Min. Suitable for high school geometry and calculus education, visualizing volume computation and spatial transformations.

GeoGebra Commands & Parameters

  1. Function(((x * (length - (2 * x))) * (width - (2 * x))), 0, Vright) → V
  2. Segment(B, C) → b
  3. Rotate(B, α, A) → B'
  4. Line(B', A) → s
  5. Line(Ax, s) → s1
  6. Segment(A, B) → a
  7. Line(C, a) → r
  8. Intersect(s, r) → D
  9. Line(Dy, r) → r1
  10. Intersect(r1, b) → Cy
  11. Segment(Dy, Cy) → c1
  12. Segment(C, D) → c
  13. Intersect(s1, c) → Dx
  14. Segment(Ax, Dx) → d1
  15. Intersect(d1, c1) → D1
  16. Line(B, s) → q
  17. Line(Bx, q) → q1
  18. Intersect(q1, c) → Cx
  19. Segment(Bx, Cx) → b1
  20. Intersect(b1, c1) → C1
  21. Line(A, B) → p
  22. Line(Ay, p) → p1
  23. Intersect(p1, b) → By
  24. Segment(Ay, By) → a1
  25. Intersect(d1, a1) → A1
  26. Intersect(b1, a1) → B1
  27. Angle(B, A, B') → β
  28. Segment(D, A) → d
  29. Polygon(A1, A2a, B2a, B1) → poly1, e, f, g, h_1
  30. Polygon(B1, B2b, C2b, C1) → poly2, i, j, k, l
  31. Polygon(C1, C2c, D2c, D1) → poly3, c_1, d_1, e_1, f_1
  32. Polygon(D1, D2d, A2d, A1) → poly4, m, n, a_1, b_1
  33. Derivative(V) → Vder
  34. Root(Vder) → tMax_1, tMax_2
  35. Min(x(tMax_1), x(tMax_2)) → tMax
  36. Segment(tMax_1, P) → g_1
  37. Intersect(c1, d1) → E
  38. Intersect(c1, b1) → F
  39. Intersect(b1, a1) → G
  40. Intersect(d1, a1) → H
  41. Polygon(E, F, G, H) → poly5, e_2, f_2, g_2, h_2