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Modifiable Solid: Square Cross Sections Parallel to yAxis

Modifiable Solid: Square Cross Sections Parallel to yAxis
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2019-04-02 08:01
Solid GeometryCalculusIntegralGeometric Construction
In collections GeoGebra 3D & AR: PreCalc & Calculus Resources Cross Sectional Specials (Calculus)
This example demonstrates a modifiable solid where cross-sections parallel to the yAxis are squares. Core mathematical concepts include integral calculus, solid geometry, and the geometric representation of functions. Construction highlights involve GeoGebra commands such as Intersect, Line, Sphere, Translate, CurveCartesian, Surface, Segment, Angle, Polygon, and Textfield. Suitable for high school and above students learning calculus and solid geometry.

GeoGebra Commands & Parameters

  1. Intersect(upper, h, (0, 5)) → B
  2. Intersect(lower, h, (0, -5)) → C
  3. Line(B, D) → i
  4. Sphere(B, d) → e
  5. Translate(C, Vector[(0, 0, d)]) → C'
  6. CurveCartesian(t, lower(t), upper(t) - lower(t), t, a, b) → k
  7. CurveCartesian(t, upper(t), upper(t) - lower(t), t, a, b) → l
  8. Surface(u, lower(u), (v * (upper(u) - lower(u))), u, a, b, v, 0, 1) → j
  9. Surface(u, upper(u), (v * (upper(u) - lower(u))), u, a, b, v, 0, 1) → m
  10. Surface(u, (v * lower(u)) + ((1 - v) * upper(u)), upper(u) - lower(u), u, a, b, v, 0, 1) → n
  11. Segment(C, B) → p
  12. Segment(C, B) → q
  13. Segment(C, C') → r
  14. Intersect(i, e) → E, F
  15. Segment(C', F) → s
  16. Segment(F, B) → t
  17. Angle(B, C, C') → α
  18. Angle(C, C', F) → β
  19. Angle(C', F, B) → γ
  20. Angle(F, B, C) → δ
  21. Intersect(upper, q, (0, 5)) → G
  22. Polygon(C, G, F, C') → q1, c_1, g_1, f_1, c'
  23. Polygon(K, J, L, M) → q2, k_1, j_1, l_1, m_1
  24. Segment(M, L) → c
  25. Segment(L, J) → p_1
  26. Segment(J, K) → q_1
  27. Segment(K, M) → r_1
  28. Segment(H, I) → s_1
  29. Polygon(Q, P, R, S) → q3, q_2, p_2, r_2, s_2
  30. Textfield(upper) → InputBox1
  31. Textfield(lower) → InputBox2
  32. Segment(P, R) → f
  33. Segment(R, S) → g
  34. Segment(S, Q) → i_1
  35. Textfield(a) → InputBox3
  36. Textfield(b) → InputBox4