MathPlotAI Logo MathPlotAI

Ball in a Glass of Water

Ball in a Glass of Water
Loading the math board and drawing, please wait…
2016-01-02 01:43
TrigonometrySolid GeometryGeometric ConstructionGraphing
This example demonstrates the geometric phenomenon of a sphere partially submerged in water within a glass. It involves core mathematical concepts such as volume calculation, sphere surface area, percentages, and natural numbers. The construction utilizes GeoGebra commands and objects like RotateText, Circle, Sphere, Cylinder, and Intersect, as outlined in the summary. It is suitable for high school students studying solid geometry, volume calculations, and spatial reasoning.

GeoGebra Commands & Parameters

  1. RotateText("uStas\;\&\,Т.С.", 90°) → надпись01
  2. Circle(Q - (0, 0, 2), 0.4, zAxis) → ϕ
  3. Cone(ϕ, 2) → d, c, a_1
  4. Segment(A, B) → plechy
  5. Segment(A, A_1) → a
  6. Segment(B, B_1) → b
  7. Circle(A_1, m, zAxis) → ω_a
  8. Cylinder(ω_a, (2 * m)) → φ_a, ω'_a, a_a
  9. Circle(B_1, m, zAxis) → ω_b
  10. Cylinder(ω_b, (2 * m)) → φ_b, ω'_b, a_b
  11. Sphere(A_1 + (0, 0, R), R) → ψ_a
  12. Sphere(B_1 + (0, 0, R), R) → ψ_b
  13. Line(A_2 + (0, 0, (0.5 * p)), xAxis) → d_a
  14. Line(B_2 + (0, 0, (0.5 * p)), xAxis) → d_b
  15. Parabola(F_a, d_a) → λ_a
  16. Parabola(F_b, d_b) → λ_b
  17. Intersect(Line[A_1 + (0, 0, h), xAxis], λ_a, 2) → G_a
  18. Intersect(Line[B_1 + (0, 0, h), xAxis], λ_b, 1) → G_b
  19. CurveCartesian(x(A_2) - i, 0, z(A_2) - (0.5 * i^(2) / p), i, 0, ii) → θ_a
  20. CurveCartesian(x(B_2) + i, 0, z(B_2) - (0.5 * i^(2) / p), i, 0, ii) → θ_b
  21. Cylinder(ω_a, h) → ϕ_a, ω''_a, i
  22. Intersect(f, xAxis, 2) → F
  23. IntersectPath(z = z(B_1) + h_3, ψ_b) → θ
  24. Point(θ, 0.5) → U
  25. Surface(x(A_1) + ((R * sin(i)) * sin(j)), y(A_1) + ((R * sin(i)) * cos(j)), z(A_1) + R + (R * cos(i)), i, α_1, (2 * π) - α_1, j, 0, 6.2831853072) → ψ'_a
  26. Surface(x(A_1) + ((R * sin(i)) * sin(j)), y(A_1) + ((R * sin(i)) * cos(j)), z(A_1) + R + (R * cos(i)), i, 1.5707963267948966, 4.71238898038469, j, 0, 3.141592653589793) → ψ''_a
  27. Surface(x(A_1) + ((R * sin(i)) * sin(j)), y(A_1) + ((R * sin(i)) * cos(j)), z(A_1) + R + (R * cos(i)), i, π - α_1, π + α_1, j, 0, 6.2831853072) → ψ'''_a
  28. Cylinder(ω''_a, h') → ϕ'_a, ω'''_a, g
  29. Cylinder(ω_b, (h' * h_3 / h_4)) → ϕ_b, ω''_b, j
  30. Sphere(B_3, R) → ψ'_b
  31. Translate(θ, Vector[(0, 0, h_5 + (1.5 * p))]) → θ'
  32. Cylinder(ω_b, (h' * h_3 / h_4) + h_5 + (1.5 * p)) → ϕ'_b, e, k
  33. Translate(U, Vector[B_1, A_1]) → U_a
  34. Circle(A_1 + (0, 0, z(U_a) - z(A_1)), Radius[θ], zAxis) → θa