MathPlotAI Logo MathPlotAI

Animating Height vs. Time for a Filling Hollow Sphere

Animating Height vs. Time for a Filling Hollow Sphere
Loading the math board and drawing, please wait…
2012-11-26 01:58
FunctionSolid GeometryGeometric ConstructionSlider AnimationGraphing
This example animates the height of water in a hollow sphere as it fills over time, displaying the corresponding function graph. It involves key concepts such as functional relationships, similar triangles, correlation, and tangent lines. The GeoGebra construction uses commands like Line, Mirror, Circle, OrthogonalLine, Intersect, CircumcircleArc, Ellipse, Segment, and Point, with a slider controlling the filling process. It is suitable for high‑school or university students learning solid geometry, functions, and geometric modeling.

GeoGebra Commands & Parameters

  1. Line((0, 0), (1, 1)) → a
  2. Mirror(g, a) → g_2
  3. Circle((-2, 1), 1) → c
  4. OrthogonalLine(A, yAxis) → d
  5. Intersect(g_1, d, 2) → C
  6. Line((y(C), x(C)), xAxis) → e
  7. Intersect(c, e) → B, D
  8. Intersect(c, xAxis, 1) → E
  9. CircumcircleArc(D, E, B) → h
  10. Ellipse(F, G, 1) → p
  11. Segment(B, D) → i
  12. Intersect(p, e) → I, J
  13. Ellipse(I, J, i / 2) → k
  14. Segment((-3, 1), (-1, 1)) → j
  15. Intersect(p, j) → E_1, E_2
  16. Ellipse(E_1, E_2, 1) → q
  17. Point(c) → K
  18. Point(c) → L
  19. Point(c) → M
  20. CircumcircleArc(K, L, M) → r
  21. Ellipse(K_1, M_1, r / 2) → s