MathPlotAI Logo MathPlotAI

Modifiable Solid with Semicircular Cross Sections Parallel to yAxis

Modifiable Solid with Semicircular Cross Sections Parallel to yAxis
Loading the math board and drawing, please wait…
2019-04-02 22:43
FunctionSolid GeometryCalculus
In collections GeoGebra 3D & AR: PreCalc & Calculus Resources Cross Sectional Specials (Calculus)
This example demonstrates constructing a modifiable solid with semicircular cross sections parallel to the yAxis. Key mathematical concepts include integral calculus and solid geometry. Using GeoGebra commands such as CurveCartesian, Surface, and Rotate, the relationship between the cross-sectional shape and the overall solid's volume is visually illustrated. Suitable for high school and above students studying solid geometry and calculus.

GeoGebra Commands & Parameters

  1. Segment(H, I) → s_1
  2. Midpoint(s_1) → E
  3. Segment(J, K) → q_1
  4. Midpoint(q_1) → F
  5. Intersect(upper, h, (0, 5)) → B
  6. Intersect(lower, h, (0, -8)) → C
  7. Segment(C, B) → q
  8. Intersect(upper, q, (0, 5)) → G
  9. Midpoint(C, G) → T
  10. Line(B, D) → i
  11. Sphere(B, d) → e
  12. Segment(C, B) → p
  13. Textfield(upper) → InputBox1
  14. Textfield(lower) → InputBox2
  15. Textfield(a) → InputBox3
  16. Textfield(b) → InputBox4
  17. Segment(C, G) → k_1
  18. Midpoint(J, K) → Z
  19. Midpoint(Q, P) → A_1
  20. CurveCartesian(b, y(Z) + ((y(J) - y(Z)) * cos(u)), ((y(J) - y(Z)) * sin(u)), u, 0, pi) → f
  21. CurveCartesian(a, y(A_1) + ((y(Q) - y(A_1)) * cos(u)), ((y(Q) - y(A_1)) * sin(u)), u, 0, pi) → c
  22. Surface(u, (0.5 * (upper(u) + lower(u))) + ((0.5 * (upper(u) - lower(u))) * cos(v)), ((0.5 * (upper(u) - lower(u))) * sin(v)), u, a, b, v, 0, pi) → g
  23. Midpoint(C, G) → W
  24. CurveCartesian(x(W), (0.5 * (y(G) + y(C))) + ((0.5 * (y(G) - y(C))) * cos(u)), ((0.5 * (y(G) - y(C))) * sin(u)), u, 0, pi) → j
  25. Line(W, B_1) → k
  26. Sphere(W, G) → l
  27. Intersect(k, l) → C_1, D_1
  28. Rotate(D_1, ((-pi)) / 2, W) → E_1
  29. Rotate(D_1, pi / 2, W) → F_1
  30. CircleArc(W, E_1, F_1, xOyPlane) → r
  31. Line(W, E_1) → m
  32. Rotate(r, pi / 2, W, m) → r'
  33. Midpoint(q_1) → G_1
  34. Midpoint(s_1) → H_1
  35. Line(G_1, G_1 + (1, 0, 0)) → n
  36. Line(H_1, H_1 + (1, 0, 0)) → s
  37. Sphere(G_1, J) → o
  38. Intersect(n, o) → I_1, J_1
  39. Sphere(H_1, Q) → t
  40. Intersect(s, t) → K_1, L_1
  41. Rotate(J_1, ((-pi)) / 2, G_1) → M_1
  42. Rotate(J_1, pi / 2, G_1) → N_1
  43. CircleArc(G_1, M_1, N_1, xOyPlane) → c_1
  44. Rotate(c_1, ((-pi)) / 2, G_1, Line[G_1, N_1]) → e_1
  45. Rotate(L_1, ((-pi)) / 2, H_1) → O_1
  46. Rotate(L_1, pi / 2, H_1) → P_1
  47. CircleArc(H_1, O_1, P_1, xOyPlane) → d_1
  48. Rotate(d_1, ((-pi)) / 2, H_1, Line[H_1, Q]) → f_1