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Custom Cuboid: Dynamic Dimension Adjustment and Volume/Surface Area Calculation

Custom Cuboid: Dynamic Dimension Adjustment and Volume/Surface Area Calculation
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2015-04-13 13:47
Solid GeometryGeometric ConstructionSlider Animation
This example demonstrates how to dynamically adjust the dimensions of a cuboid to calculate and visualize its volume and surface area. The key mathematical concepts involve the volume formula (V = length × width × height) and surface area formula (S = 2×(length×width + length×height + width×height)). Construction involves using GeoGebra commands such as Segment, OrthogonalLine, Intersect, Ray, Circle, Line, Vector, and Polygon to build the cuboid, along with a slider for dynamic adjustment. Suitable for middle school and above students to understand three-dimensional geometry and practical applications.

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

AI Drawing Prompt Reference

Draw a cuboid with adjustable length, width, and height, and display its volume and surface area. Use a slider to dynamically change the dimensions of the cuboid, visualizing the results through the calculation formulas (volume = length × width × height, surface area = 2×(length×width + length×height + width×height)). First, construct the base and sides of the cuboid, then determine the top vertices by intersecting rays with circles, and finally connect all vertices to form the faces of the cuboid, distinguishing them with different colors.
The prompt above was compiled from the original drawing commands and is for reference only.