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Cavalieri's Principle and Sphere Volume

Cavalieri's Principle and Sphere Volume
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2015-06-15 17:07
Solid GeometryCalculusGeometric Construction
This example demonstrates how to compute the volume of a sphere using Cavalieri's principle. It involves core concepts like Cavalieri's principle, sphere, cone, plane sections, and is constructed using GeoGebra commands such as Point, Line, OrthogonalLine, Sphere, Cone, Plane, IntersectPath, Center, Segment, Circle. Suitable for high school solid geometry and introductory calculus learning.

GeoGebra Commands & Parameters

  1. Point(xAxis) → A
  2. Line(A, O) → b_1
  3. Point(xAxis) → F
  4. OrthogonalLine(A, xOyPlane) → b
  5. Line(F, b) → j
  6. Sphere(O, r) → a
  7. Point(b) → B
  8. Cone(B, C, r) → c, d, e
  9. Plane(G, xOyPlane) → f
  10. IntersectPath(f, a) → g
  11. IntersectPath(f, c) → h
  12. Plane(O, xOyPlane) → i
  13. Plane(O, xOyPlane) → l
  14. Center(h) → H
  15. Center(g) → I
  16. Point(g) → J
  17. Point(h) → K
  18. Segment(I, J) → m
  19. Segment(H, K) → n
  20. Point(xAxis) → M
  21. Point(xAxis) → N
  22. Circle(X, n, zAxis) → c_1
  23. Center(c_1) → L
  24. Center(c_1) → xx
  25. Circle(xx, rr, b) → s
  26. Point(b_1) → D
  27. OrthogonalLine(D, xOyPlane) → t
  28. Point(t) → E
  29. Point(b_1) → P
  30. OrthogonalLine(P, xOyPlane) → a_1
  31. Point(a_1) → Q