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Modifiable Solid: Isosceles Right Triangle Cross Sections Parallel to yAxis

Modifiable Solid: Isosceles Right Triangle Cross Sections Parallel to yAxis
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2019-04-02 08:40
Solid GeometryCalculusGeometric Construction
In collections GeoGebra 3D & AR: PreCalc & Calculus Resources Cross Sectional Specials (Calculus)
This example demonstrates how to create a modifiable solid in calculus, showing cross sections that are isosceles right triangles parallel to the y-axis. The key mathematical concepts involve solid geometry, cross-sectional area calculation, and function graphing. Construction requires using GeoGebra commands such as Intersect, Line, Sphere, Translate, and CurveCartesian. It is suitable for high school students or college students learning calculus and geometry.

GeoGebra Commands & Parameters

  1. Intersect(upper, h, (-0.14282132839208828, 9.997960206815632)) → B
  2. Intersect(lower, h, (-0.14282132839208828, -7.929316413566142)) → 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. Surface(u, lower(u), (v * (upper(u) - lower(u))), u, a, b, v, 0, 1) → j
  8. Segment(C, B) → p
  9. Segment(C, B) → q
  10. Segment(C, C') → r
  11. Angle(B, C, C') → α
  12. Intersect(upper, q, (-0.14282132839208825, 9.997960206815632)) → G
  13. Polygon(C, G, C') → q1, f_1, g_1, a_1
  14. Polygon(K, J, M) → q2, c, i_1, j_1
  15. Segment(J, K) → q_1
  16. Segment(K, M) → r_1
  17. Segment(H, I) → s_1
  18. Polygon(Q, P, R) → q3, m, s, t
  19. Textfield(upper) → InputBox1
  20. Textfield(lower) → InputBox2
  21. Segment(P, R) → f
  22. Textfield(a) → InputBox3
  23. Textfield(b) → InputBox4
  24. Segment(C', G) → n_1
  25. Surface(u, (v * lower(u)) + ((1 - v) * upper(u)), (v * (upper(u) - lower(u))), u, a, b, v, 0, 1) → n
  26. Segment(J, M) → l
  27. Point(f) → E
  28. Segment(E, Q) → g