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Volume of a Sphere by Diah Vialita Dewi

Volume of a Sphere by Diah Vialita Dewi
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2018-08-29 16:26
FunctionCoordinate GeometrySolid Geometry
This example demonstrates how to construct a sphere and calculate its volume using GeoGebra. Key mathematical concepts include the volume formula for a sphere in solid geometry. The construction uses commands such as Sphere, IntersectPath, Intersect, Line, Rotate, Sequence, Point, Segment, OrthogonalLine, CircleSector, and Pyramid.

GeoGebra Commands & Parameters

  1. Sphere(A, r) → a
  2. IntersectPath(b, a) → c
  3. Intersect(yAxis, c, 1) → B
  4. Intersect(xAxis, c, 1) → D
  5. Intersect(yAxis, c, 2) → C
  6. Intersect(xAxis, c, 2) → E
  7. Line(C, B) → g
  8. Line(E, D) → f
  9. Rotate(c, 90°, f) → c'
  10. Sequence(Rotate[c, ((i * 360) * ° / n), g], i, 1, n) → L_1
  11. Point(L_1) → F
  12. Intersect(zAxis, c', 2) → G_1
  13. Intersect(zAxis, c') → I, I_1
  14. Segment(I, E) → h
  15. Segment(E, C) → i
  16. Segment(C, I) → j
  17. OrthogonalLine(C, h, space) → k
  18. Intersect(k, h) → G
  19. Segment(G, C) → l
  20. Segment(I, E) → dx
  21. Segment(C, G) → dy
  22. CircleSector(J, A, H) → d
  23. Pyramid(A, H, J, K) → e, faceAHJ, edgeJK, faceAHK, faceHJK, faceAJK, edgeAH, edgeHJ, edgeAJ, edgeAK, edgeHK
  24. 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
  25. 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

AI Drawing Prompt Reference

Construct a three-dimensional sphere, create cross-section circles passing through the coordinate axes on the sphere, and generate a solid of revolution by rotating the cross-section around an axis; draw line segments through the intersection points with the coordinate axes on the cross-section, construct perpendicular lines to these segments; create circular sectors on the cross-section, and fill the sphere with multiple pyramids to demonstrate the volume calculation of the sphere.
The prompt above was compiled from the original drawing commands and is for reference only.