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Volume of a Cuboid by Nicolas ERDRICH

Volume of a Cuboid by Nicolas ERDRICH
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2014-01-15 04:25
Coordinate GeometrySolid GeometryGeometric Construction
This example demonstrates how to calculate the volume of a cuboid using geometric construction. Key math concepts include solid geometry and geometric construction. It utilizes commands such as Line, OrthogonalLine, Circle, Intersect, Rotate, Angle, Segment, Midpoint, Polygon, Sequence in GeoGebra. Suitable for middle school and above students learning solid geometry.

GeoGebra Commands & Parameters

  1. Line(A, xAxis) → a
  2. OrthogonalLine(A, a) → q_4
  3. Circle(A, 2) → r
  4. Intersect(r, q_4, 2) → E
  5. Intersect(r, a, 2) → B
  6. OrthogonalLine(E, q_4) → s
  7. OrthogonalLine(B, a) → t
  8. Intersect(s, t) → F
  9. Rotate(F, 45*°, E) → S'
  10. Angle(F, E, S') → α
  11. Segment(E, S') → i_1
  12. Segment(E, F) → j_1
  13. Midpoint(j_1) → T
  14. Circle(E, T) → k_1
  15. Intersect(k_1, i_1, 1) → H
  16. Segment(E, H) → p_1
  17. Line(H, j_1) → q_1
  18. Line(F, p_1) → r_1
  19. Intersect(q_1, r_1) → V
  20. Segment(A, E) → s_1
  21. Segment(F, B) → t_1
  22. Line(B, r_1) → a_2
  23. Line(V, s_1) → b_2
  24. Intersect(a_2, b_2) → W
  25. Polygon(A, B, F, E) → poly1, p_2, r_2, s_2, q_2
  26. Polygon(B, W, V, F) → poly2, r_3, w, v, s_3
  27. Polygon(E, F, V, H) → poly3, q_3, s_4, v_1, u
  28. Sequence(Sequence[Polygon[Translate[E, Vector[l * Vector[B, A] + m * Vector[E, H]]], Translate[F, Vector[l * Vector[B, A] + m * Vector[E, H]]], Translate[V, Vector[l * Vector[B, A] + m * Vector[E, H]]], Translate[H, Vector[l * Vector[B, A] + m * Vector[E, H]]]], l, 0, o], m, 0, q) → liste3
  29. Sequence(Sequence[Polygon[Translate[B, Vector[l * Vector[E, A] + m * Vector[E, H]]], Translate[W, Vector[l * Vector[E, A] + m * Vector[E, H]]], Translate[V, Vector[l * Vector[E, A] + m * Vector[E, H]]], Translate[F, Vector[l * Vector[E, A] + m * Vector[E, H]]]], l, 0, p], m, 0, q) → liste2
  30. Sequence(Sequence[Polygon[Translate[A, Vector[k * Vector[B, A] + l * Vector[E, A]]], Translate[B, Vector[k * Vector[B, A] + l * Vector[E, A]]], Translate[F, Vector[k * Vector[B, A] + l * Vector[E, A]]], Translate[E, Vector[k * Vector[B, A] + l * Vector[E, A]]]], k, 0, o], l, 0, p) → liste

AI Drawing Prompt Reference

Draw a cuboid to demonstrate the calculation of its volume. Start by constructing the base and sides of the cuboid, then rotate a part of the base to form the top. Label key points, lines, and angles, and use different colors to distinguish each part. Finally, stack multiple parallelograms to represent the volume of the cuboid, showing the geometric construction process.
The prompt above was compiled from the original drawing commands and is for reference only.