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Cylinder Volume Demonstration

Cylinder Volume Demonstration
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2020-08-19 16:45
CirclePolygonSolid GeometryGeometric Construction
① This example shows how to construct a cylinder geometrically and visually illustrate its volume calculation. ② Core mathematical concepts include the solid‑geometry formula for cylinder volume, the relationship between base‑circle area, height, and volume, and the interplay between polygons and circles. ③ Construction highlights: the model is built with GeoGebra commands Segment, Polygon, Ellipse, OrthogonalLine, Circle, Intersect, Point, Line, and Midpoint, creating objects such as base circles (r_1, r_2), side rectangles (l_1, w_1, l_2, w_2), vertices (A_1, B_1, C_1, D_1, A_2, B_2, C_2, D_2), polygons (poly1, poly2), and auxiliary points (E, E_1, etc.). ④ Suitable for middle‑school geometry (grades 7‑9) and high‑school solid‑geometry review, and serves as a ready‑to‑use GeoGebra teaching demo.

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), D + ((-0.05), 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), M + ((-0.055), 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), G + (0.05, 0)) → l
  46. Segment(R_2 + (0.055, 0), O + (0.055, 0)) → j_1

AI Drawing Prompt Reference

Draw a cylinder to demonstrate its volume calculation. Start by creating two equal circles as bases, then connect the edges of the circles to form the lateral surface. Use the lateral surface and bases to illustrate the volume formula of a cylinder, which is the base area multiplied by the height. Represent the lateral surface and bases as polygons and emphasize geometric relationships using auxiliary lines and perpendiculars.
The prompt above was compiled from the original drawing commands and is for reference only.