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Modifiable Solid: Rectangular Cross Sections Parallel to yAxis

Modifiable Solid: Rectangular Cross Sections Parallel to yAxis
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2019-07-07 02:28
Coordinate GeometrySolid GeometryCalculus
In collections Cross Sectional Specials (Calculus)
This example demonstrates a modifiable solid where cross sections parallel to the yAxis are rectangles, with height equal to w times the base. It involves core mathematical concepts such as integral calculus, solid geometry, and coordinate geometry. Construction highlights include using GeoGebra commands like Line, Sphere, Translate, Segment, Angle, Intersect, Polygon, Textfield, CurveCartesian, and Surface. Suitable for high school and above students learning calculus and solid geometry.

GeoGebra Commands & Parameters

  1. Line(B, D) → i
  2. Sphere(B, (d * w)) → e
  3. Translate(C, Vector[(0, 0, (d * w))]) → C'
  4. Segment(C, B) → p
  5. Segment(C, B) → q
  6. Segment(C, C') → r
  7. Segment(C', F) → s
  8. Segment(F, B) → t
  9. Angle(B, C, C') → α
  10. Angle(C, C', F) → β
  11. Angle(C', F, B) → γ
  12. Angle(F, B, C) → δ
  13. Intersect(upper, q, (1.8739599999999998, 3.091206439139138)) → G
  14. Polygon(C, B, F, C') → q1, f_1, g_1, n_1, a_1
  15. Polygon(K, J, L, M) → q2, k_1, j_1, l_1, m_1
  16. Segment(M, L) → c
  17. Segment(L, J) → p_1
  18. Segment(J, K) → q_1
  19. Segment(K, M) → r_1
  20. Segment(H, I) → s_1
  21. Polygon(Q, P, R, S) → q3, q_2, p_2, r_2, s_2
  22. Textfield(upper) → InputBox1
  23. Textfield(lower) → InputBox2
  24. Segment(P, R) → f
  25. Segment(R, S) → g
  26. Segment(S, Q) → i_1
  27. Textfield(a) → InputBox3
  28. Textfield(b) → InputBox4
  29. CurveCartesian(t, lower(t), ((upper(t) - lower(t)) * w), t, a, b) → k
  30. CurveCartesian(t, upper(t), ((upper(t) - lower(t)) * w), t, a, b) → l
  31. Surface(u, lower(u), ((v * w) * (upper(u) - lower(u))), u, a, b, v, 0, 1) → j
  32. Surface(u, (v * lower(u)) + ((1 - v) * upper(u)), (w * (upper(u) - lower(u))), u, a, b, v, 0, 1) → n
  33. Surface(u, upper(u), ((v * w) * (upper(u) - lower(u))), u, a, b, v, 0, 1) → m