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Sphere Volume Calculation Demo by 胡天翼

Sphere Volume Calculation Demo by 胡天翼
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2018-12-12 10:23
Solid GeometryCalculusGeometric ConstructionGraphing
This example dynamically demonstrates the volume relationships between a sphere, cylinder, and cone, visually showing the derivation of the sphere volume formula. Core mathematical concepts include solid geometry volume calculation, geometric body relationships, and integral concepts. GeoGebra commands and objects used in construction include Sphere, Cylinder, Cone, Segment, Point, OrthogonalPlane, IntersectPath, Corner, Intersect, and Line. Suitable for high school solid geometry teaching and student understanding of volume formulas.

GeoGebra Commands & Parameters

  1. Sphere(A, B) → a
  2. Cylinder(C, D, 2) → b, c, d, e
  3. Cone(D, E, 2) → f, g, h
  4. Cone(C, E, 2) → i, k, j
  5. Segment(G, F) → l
  6. Point(l) → H
  7. OrthogonalPlane(H, l) → m
  8. IntersectPath(m, a) → p
  9. IntersectPath(m, b) → q
  10. Corner(q) → M, N, O, P
  11. IntersectPath(m, i) → r
  12. IntersectPath(m, f) → s
  13. Corner(s) → I, J, K, L
  14. Segment(C, D) → n
  15. Segment(Q, B) → t
  16. Intersect(t, m) → R
  17. Intersect(n, m) → S
  18. Line(H, S) → a_1
  19. Intersect(a_1, p) → T, U
  20. Segment(R, T) → b_1
  21. Segment(R, A) → c_1
  22. Segment(A, T) → d_1
  23. Intersect(a_1, q) → V, W
  24. Intersect(a_1, r) → Z, A_1
  25. Segment(Z, E) → e_1
  26. Segment(E, S) → f_1
  27. Segment(S, V) → g_1

AI Drawing Prompt Reference

Draw a sphere, cylinder, and cone with the same base and height, demonstrating the volume relationships between them and visually deriving the sphere volume formula. A point moves on the sphere's surface, generating a path that intersects the sphere, cylinder, and cone, forming auxiliary line segments and intersection points, ultimately creating a geometric construction that clearly shows the derivation of the volume formula.
The prompt above was compiled from the original drawing commands and is for reference only.