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Solids with Given Cross Sections

Solids with Given Cross Sections
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2019-03-06 06:48
Solid GeometryCalculusIntegral
This example demonstrates solids with given cross sections. It involves the concept of integral calculus, constructing different shapes of cross sections to generate the solid. Commands used include Point, IndexOf, CurveCartesian, Surface, Polygon, OrthogonalPlane, OrthogonalLine, CircleSector, etc. Suitable for high school or university calculus courses on solid geometry.

GeoGebra Commands & Parameters

  1. Point(xAxis) → A
  2. Point(xAxis) → B
  3. IndexOf(SelectedElement[shape], shape) → a
  4. CurveCartesian(t, g(t) + (f(t) - g(t)) / 2, ((f(t) - g(t)) / 2 * sqrt(3)), t, x(A), x(B)) → b
  5. Surface(t, (u * g(t)) + ((1 - u) * y(b(t))), ((1 - u) * z(b(t))), t, x(A), x(B), u, 0, 1) → c
  6. Surface(t, (u * f(t)) + ((1 - u) * y(b(t))), ((1 - u) * z(b(t))), t, x(A), x(B), u, 0, 1) → d
  7. CurveCartesian(t, f(t), f(t) - g(t), t, x(A), x(B)) → h
  8. CurveCartesian(t, g(t), f(t) - g(t), t, x(A), x(B)) → i
  9. Surface(t, f(t), (u * z(h(t))), t, x(A), x(B), u, 0, 1) → j
  10. Surface(t, g(t), (u * z(i(t))), t, x(A), x(B), u, 0, 1) → k
  11. Surface(t, (u * g(t)) + ((1 - u) * f(t)), z(i(t)), t, x(A), x(B), u, 0, 1) → l
  12. CurveCartesian(t, f(t), f(t) - g(t), t, x(A), x(B)) → m
  13. Surface(t, (u * g(t)) + ((1 - u) * f(t)), ((1 - u) * (f(t) - g(t))), t, x(A), x(B), u, 0, 1) → n
  14. Surface(t, f(t), ((1 - u) * (f(t) - g(t))), t, x(A), x(B), u, 0, 1) → o
  15. CurveCartesian(t, g(t), f(t) - g(t), t, x(A), x(B)) → p
  16. Surface(t, (u * f(t)) + ((1 - u) * g(t)), ((1 - u) * (f(t) - g(t))), t, x(A), x(B), u, 0, 1) → q
  17. Surface(t, g(t), ((1 - u) * (f(t) - g(t))), t, x(A), x(B), u, 0, 1) → r
  18. CurveCartesian(t, (f(t) + g(t)) / 2, 0, t, x(A), x(B)) → s
  19. Surface(t, y(s(t)) + ((f(t) - g(t)) / 2 * cos(u)), ((f(t) - g(t)) / 2 * sin(u)), t, x(A), x(B), u, 0, π) → t_1
  20. Polygon((t, g(t), 0), (t, f(t), 0), b(t)) → t1, e, f_1, g_1
  21. Polygon((t, f(t), 0), h(t), i(t), (t, g(t), 0)) → q1, h_1, i_1, j_1, k_1
  22. Polygon((t, f(t), 0), m(t), (t, g(t), 0)) → t2, l_1, m_1, n_1
  23. Polygon((t, f(t), 0), (t, g(t), 0), p(t)) → t3, p_1, q_1, r_1
  24. CurveCartesian(t, ((f(t) - g(t)) / 2 * cos(u)) + y(s(t)), ((f(t) - g(t)) / 2 * sin(u)), u, 0, π) → u
  25. OrthogonalPlane(C, xAxis) → v
  26. OrthogonalLine(C, v) → s_1
  27. Point(u) → D
  28. Point(u) → E
  29. CircleSector(C, D, E, xOyPlane) → c_1