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Sphere Volume Demonstration by Sugeng Suprayogi

Sphere Volume Demonstration by Sugeng Suprayogi
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2018-08-31 05:52
Solid GeometryGeometric Construction
This example demonstrates the calculation of a sphere's volume. Key mathematical concepts include the volume formula for a sphere and its application. Using GeoGebra commands such as Sphere, IntersectPath, Intersect, etc., the construction process of the sphere is dynamically shown. Suitable for high 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(B, C) → g
  7. Rotate(c, 90°, f) → c'
  8. Intersect(c, c') → F, G_1, ,
  9. Sequence(Rotate[c, ((i * 360) * ° / n), g], i, 1, n) → L_1
  10. Point(L_1) → I
  11. Segment(I, F) → h
  12. Segment(I, C) → i
  13. Segment(C, F) → j
  14. OrthogonalLine(C, h, space) → k
  15. Intersect(h, k) → G
  16. Segment(C, G) → l
  17. Segment(I, E) → dx
  18. Segment(C, G) → dy
  19. Polygon(A, H, J) → t1, j_1, a_1, h_1
  20. Pyramid(t1, r) → d, K, faceAHK, faceHJK, faceAJK, edgeAK, edgeHK, edgeJK
  21. CircleSector(J, A, H, xOyPlane) → e
  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