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Cylinder Volume Calculation Demo by Diah Vialita Dewi

Cylinder Volume Calculation Demo by Diah Vialita Dewi
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2018-08-29 16:24
Solid GeometryGeometric Construction
This example demonstrates the calculation and visualization of a cylinder's volume. It involves core math concepts like the cylinder volume formula, circle area calculation, and spatial geometry. Construction highlights include GeoGebra commands such as Cylinder, Point, Intersect, Segment, Ray, Line, Polygon, Sequence, and OrthogonalLine. Suitable for high school mathematics teaching or self-learning to understand volume calculations in solid geometry.

GeoGebra Commands & Parameters

  1. Cylinder(A, B, r) → a, c, d, b
  2. Point(d) → C
  3. Intersect(yAxis, c, 2) → D
  4. Segment(B, C) → g
  5. Ray(A, B) → f
  6. Point(f) → E
  7. Line(E, f) → i
  8. Line(D, i) → j
  9. Segment(A, D) → k
  10. Segment(C, D) → l
  11. Polygon(A, B, C, D) → q1, a_1, b_1, c_1, d_1
  12. Sequence(Rotate[C, ((i * 360) * ° / n), B], i, 0, n) → L_1
  13. Sequence(Rotate[D, ((i * 360) * ° / n), A], i, 0, n) → L_2
  14. Sequence(Segment[Rotate[C, ((i * 360) * ° / n), B], Rotate[D, ((i * 360) * ° / n), A]], i, 0, n) → L_3
  15. Sequence(Segment[Rotate[B, ((i * 360) * ° / n), B], Rotate[C, ((i * 360) * ° / n), B]], i, 0, n) → L_4
  16. Sequence(Segment[Rotate[A, ((i * 360) * ° / n), B], Rotate[D, ((i * 360) * ° / n), B]], i, 0, n) → L_5
  17. Sequence(Rotate[q1, ((i * 360) * ° / n), j], i, 0, n) → L_6
  18. Point(L_1) → G
  19. Segment(C, G) → m
  20. OrthogonalLine(B, m, space) → p
  21. Intersect(p, m) → H
  22. Segment(B, H) → q
  23. Segment(C, H) → dx
  24. Segment(B, H) → dy
  25. Sequence(CircleSector[((j * dx) + dx / 2, dy), ((j * dx) + 0, 0), ((j * dx) + dx, 0)], j, 0, n / 2 - 1) → L_7
  26. Sequence(CircleSector[((j * dx), 0), ((j * dx) + dx / 2, dy), ((j * dx) + ((-dx)) / 2, dy)], j, 1, n / 2) → L_8
  27. Sequence(CircleSector[((j * dx) + dx / 2, dy, h), ((j * dx) + 0, 0, h), ((j * dx) + dx, 0, h), xOyPlane], j, 0, n / 2 - 1) → L_9
  28. Sequence(CircleSector[((j * dx), 0, h), ((j * dx) + dx / 2, dy, h), ((j * dx) + ((-dx)) / 2, dy, h), xOyPlane], j, 1, n / 2) → L_{10}
  29. Sequence(Segment[((i * dx), 0, 0), ((i * dx), 0, h)], i, 0, n / 2) → L_{11}
  30. Sequence(Segment[((i * dx) - dx / 2, dy, 0), ((i * dx) - dx / 2, dy, h)], i, 0, n / 2 + 1) → L_{12}
  31. Sequence(Polygon[((((2 * i) - 1) * dx / 2), dy, 0), ((((2 * i) - 1) * dx / 2), dy, h), ((i * dx), 0, h), ((i * dx), 0, 0)], i, 1, n / 2) → L_{13}
  32. Sequence(Polygon[((((2 * i) + 1) * dx / 2), dy, h), ((((2 * i) + 1) * dx / 2), dy, 0), ((i * dx), 0, 0), ((i * dx), 0, h)], i, 1, n / 2) → L_{14}