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Sphere Volume Demonstration

Sphere Volume Demonstration
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2018-09-02 16:42
Solid GeometryGeometric Construction
This example demonstrates the calculation of a sphere's volume. Key mathematical concepts include the volume formula for a sphere in solid geometry. Using GeoGebra commands such as Sphere, IntersectPath, Intersect, etc., the construction process of the sphere is visually illustrated. Suitable for middle school students learning solid geometry.

GeoGebra Commands & Parameters

  1. Sphere(A, r) → a
  2. IntersectPath(b, a) → c
  3. Intersect(yAxis, c) → B, C
  4. Intersect(xAxis, c) → D, E
  5. Line(D, E) → f
  6. Line(C, B) → g
  7. Rotate(c, 90°, f) → c'
  8. Intersect(c, c') → G, H, ,
  9. Sequence(Rotate[c, ((i * 360) * ° / n), g], i, 1, n) → L_1
  10. Point(L_1) → I
  11. Segment(I, G) → h
  12. Segment(I, C) → i
  13. Segment(G, C) → j
  14. OrthogonalLine(C, h, space) → k
  15. Intersect(h, k) → F
  16. Segment(C, F) → l
  17. Segment(I, E) → dx
  18. Segment(C, F) → dy
  19. CircleSector(K, A, J, xOyPlane) → d
  20. Polygon(K, A, J) → t1, j_1, k_1, a_1
  21. Pyramid(t1, L) → e, faceAKL, faceAJL, faceJKL, edgeKL, edgeAL, edgeJL
  22. Sequence(CircleSector[((((2 * i) - 1) * dx / 2), dy, 0), (((i - 1) * dx), 0, 0), ((i * dx), 0, 0), xOyPlane], i, 1, (2 * n)) → L_2
  23. Sequence(Pyramid[Polygon[(((i - 1) * dx), 0, 0), ((i * dx), 0, 0), ((((2 * i) - 1) * dx / 2), dy, 0)], r], i, 1, (2 * n)) → L_3
  24. Volume(a) → volumea
  25. PointIn(a) → Pointa

AI Drawing Prompt Reference

Draw a sphere a with radius r, then use the intersection c of the sphere and a plane to construct the cross-section of the sphere. Rotate c to get c', and find the intersection points G and H of c and c'. Then, rotate c' around c to form a series of circular sectors L_1. Select point I from L_1, and use I, G, C, and F to construct a cone e. Finally, calculate the volume of the sphere a as volumea.
The prompt above was compiled from the original drawing commands and is for reference only.