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Custom Cuboid: volume / surface area with variable lengths

Custom Cuboid: volume / surface area with variable lengths
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2016-03-21 23:45
Solid GeometryGeometric Construction
This example demonstrates a customizable cuboid for teaching volume and surface area calculations. Key math concepts include solid geometry, volume formulas, and surface area formulas. Construction highlights involve commands like Segment, OrthogonalLine, Intersect, Ray, Circle, Line, Vector, Polygon, and Sequence in GeoGebra for dynamic geometry. Suitable for middle school and above, featuring sliders for dimension adjustment, grid options, solid/transparency toggles, and shaded opposite faces.

GeoGebra Commands & Parameters

  1. Segment(A, C) → i
  2. Segment(A, B) → d
  3. OrthogonalLine(B, d) → e
  4. OrthogonalLine(C, i) → f
  5. Intersect(e, f) → D
  6. Segment(D, C) → g
  7. Segment(D, B) → h
  8. Ray(C, E) → p
  9. Ray(D, E) → q
  10. Ray(B, E) → r
  11. Circle(D, (0.6 * c)) → s
  12. Intersect(s, q) → I,
  13. Line(I, h) → j
  14. Line(I, g) → k
  15. Intersect(j, r) → F
  16. Intersect(k, p) → G
  17. Segment(F, I) → l
  18. Segment(I, G) → m
  19. Segment(F, B) → n
  20. Segment(I, D) → t
  21. Segment(G, C) → a_1
  22. Line(G, l) → b_1
  23. Line(F, m) → c_1
  24. Intersect(c_1, b_1) → H
  25. Segment(F, H) → d_1
  26. Segment(H, G) → e_1
  27. Segment(H, A) → f_1
  28. Vector(J, K) → u
  29. Polygon(F, I, G, H) → poly1, f_2, i_1, g_1, h_1
  30. Polygon(B, D, C, A) → poly2, b_2, d_2, c_2, a_2
  31. Polygon(F, B, A, H) → poly3, f_3, b_3, a_3, h_2
  32. Polygon(I, D, C, G) → poly4, i_2, d_3, c_3, g_2
  33. Polygon(F, I, D, B) → poly5, f_4, i_3, d_4, b_4
  34. Polygon(H, G, C, A) → poly6, h_3, g_3, c_4, a_4
  35. Sequence(Segment[(x(C) + (k / c * (x(G) - x(C))), y(C) + (k / c * (y(G) - y(C)))), (x(D) + (k / c * (x(I) - x(D))), y(D) + (k / c * (y(I) - y(D))))], k, 1, c - 1) → list2
  36. Sequence(Segment[(x(A) + (k / b * (x(C) - x(A))), y(A) + (k / b * (y(C) - y(A)))), (x(B) + (k / b * (x(D) - x(B))), y(B) + (k / b * (y(D) - y(B))))], k, 1, b - 1) → list3
  37. Sequence(Segment[(x(A) + (k / a * (x(B) - x(A))), y(A) + (k / a * (y(B) - y(A)))), (x(C) + (k / a * (x(D) - x(C))), y(C) + (k / a * (y(D) - y(C))))], k, 1, a - 1) → list4
  38. Sequence(Segment[(x(C) + (k / a * (x(D) - x(C))), y(C) + (k / a * (y(D) - y(C)))), (x(G) + (k / a * (x(I) - x(G))), y(G) + (k / a * (y(I) - y(G))))], k, 1, a - 1) → list5
  39. Sequence(Segment[(x(D) + (k / c * (x(I) - x(D))), y(D) + (k / c * (y(I) - y(D)))), (x(B) + (k / c * (x(F) - x(B))), y(B) + (k / c * (y(F) - y(B))))], k, 1, c - 1) → list6
  40. Sequence(Segment[(x(F) + (k / b * (x(I) - x(F))), y(F) + (k / b * (y(I) - y(F)))), (x(B) + (k / b * (x(D) - x(B))), y(B) + (k / b * (y(D) - y(B))))], k, 1, b - 1) → list1