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Comparing Cylinder Volumes

Comparing Cylinder Volumes
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2015-02-11 07:01
Solid GeometryCalculusGeometric Construction
This example demonstrates the calculation and comparison of cylinder volumes by comparing two cylinders. It involves core mathematical concepts such as the formula for cylinder volume, Pythagorean theorem, trigonometric functions, conic sections, and cuboids. The construction uses GeoGebra commands/objects like Segment, Polygon, Ellipse, OrthogonalLine, Circle, Intersect, Point, Line, and Midpoint. It is suitable for high school students studying solid geometry and analytical geometry, as well as for mathematical teaching demonstrations.

GeoGebra Commands & Parameters

  1. Segment(A_1, B_1) → a
  2. Segment(B_1, C_1) → b
  3. Segment(C_1, D_1) → c
  4. Segment(D_1, A_1) → d
  5. Polygon(A_1, B_1, C_1, D_1) → poly1, a_1, b_1, c_1, d_1
  6. Polygon(A_2, B_2, C_2, D_2) → poly2, a_2, b_2, c_2, d_2
  7. Ellipse(E, E_1, B) → f
  8. Segment(E, E_1) → g
  9. OrthogonalLine(E, g) → h
  10. Circle(E, l_1) → k
  11. Intersect(k, h) → C, D
  12. OrthogonalLine(E_1, g) → i
  13. Circle(E_1, l_1) → p
  14. Intersect(p, i) → F, G
  15. Segment(E + (-(0.05), 0.0), D + (-(0.05), 0.0)) → j
  16. Point(f) → I
  17. Segment(E, E_1) → e
  18. Line(I, j) → m
  19. Circle(I, l_1) → q
  20. Intersect(q, m) → H, J
  21. Ellipse(D, G_1, J) → r
  22. Segment(J, I) → n
  23. Polygon(E, E_1, G_1, D) → poly3, e_1, e_2, g_1, d_3
  24. Ellipse(R_1, R_2, K) → s
  25. Segment(R_1, R_2) → t
  26. OrthogonalLine(R_1, t) → f_1
  27. OrthogonalLine(R_2, t) → h_1
  28. Circle(R_1, l_2) → k_1
  29. Circle(R_2, l_2) → p_1
  30. Intersect(k_1, f_1) → L, M
  31. Intersect(p_1, h_1) → N, O
  32. Segment(R_1 + (-(0.055), 0.0), M + (-(0.055), 0.0)) → i_1
  33. Point(s) → P
  34. Line(P, i_1) → m_1
  35. Circle(P, l_2) → q_1
  36. Intersect(q_1, m_1) → Q, R
  37. Segment(P, R) → n_1
  38. Ellipse(M, O, R) → s_1
  39. Polygon(R_1, R_2, O, M) → poly4, r_3, r_4, o, m_2
  40. Midpoint(e) → S
  41. Segment(S, E_1) → ra_1
  42. Segment(R_1, R_2) → across
  43. Midpoint(across) → T
  44. Segment(T, R_2) → ra_2
  45. Segment(E_1 + (0.05, 0.0), G + (0.05, 0.0)) → l
  46. Segment(R_2 + (0.055, 0.0), O + (0.055, 0.0)) → j_1