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棱柱的体积

棱柱的体积
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2018-01-03 21:59
立体几何几何作图
本范例演示棱柱体积的计算方法。核心概念包括棱柱的定义、体积公式及其应用。通过使用GeoGebra命令如Point、Polygon、Vector、Translate等，用户可以动态调整棱柱的尺寸，直观理解体积变化。适合初中及以上学生学习几何与体积计算。

GeoGebra 命令及参数

  1. Point(Circle[A, 2]) → X
  2. Polygon(A, X, C, D) → poly1, b_6, b_5, c, h_3
  3. Vector(E, F) → u
  4. Translate(A, v) → A'
  5. Translate(X, v) → B'
  6. Translate(C, v) → C'
  7. Translate(D, v) → D'
  8. Polygon(A', B', C', D') → poly1', a', b', c', d'
  9. Polygon(B', X, A, A') → poly2, b'_1, b_1, a_1, a'_1
  10. Intersect(c', b') → G
  11. Intersect(c, b_5) → H
  12. Polygon(B', G, H, X) → poly3, b'_2, g, h_2, b_2
  13. Intersect(h_3, c) → I
  14. Intersect(d', c') → J
  15. Polygon(G, H, I, J) → poly4, g_1, h_1, i, j
  16. Polygon(J, I, A, A') → poly5, j_1, i_1, a_2, a'_2
  17. Point(Circle[K, 4]) → Y
  18. Polygon(K, Y, M, N) → poly6, b_7, l, m, h_4
  19. Point(xAxis) → O
  20. Vector(O, P) → w
  21. Translate(K, z) → K'
  22. Translate(Y, z) → L'
  23. Translate(M, z) → M'
  24. Translate(N, z) → N'
  25. Polygon(K', L', M', N') → poly6', k', l', m', n'
  26. Polygon(L', Y, K, K') → poly7, l'_1, l_1, k_1, k'_1
  27. Intersect(m', l') → Q
  28. Intersect(m, l) → R
  29. Polygon(L', Q, R, Y) → poly8, l'_2, q, r, l_2
  30. Point(m') → S
  31. Intersect(h_4, m) → T
  32. Polygon(R, Q, S, T) → poly9, r_1, q_1, s, t
  33. Polygon(T, R, Y, K) → poly10, t_1, r_2, l_3, k_2
  34. Polygon(K', S, T, K) → poly11, k'_2, s_1, t_2, k_3
  35. Point(Circle[U, 4.47213595499958]) → Z
  36. Polygon(U, Z, W) → poly12, w_1, h, b
  37. Point(xAxis) → Z_1
  38. Vector(Z_1, A_1) → p
  39. Translate(U, z_1) → U'
  40. Translate(Z, z_1) → V'
  41. Translate(W, z_1) → W'
  42. Polygon(U', V', W') → poly12', w', u', v'
  43. Intersect(b, h) → B_1
  44. Intersect(v', u') → C_1
  45. Polygon(U', U, B_1, C_1) → poly13, u'_1, u_2, b_3, c_1
  46. Polygon(U', U, Z, V') → poly14, u'_2, u_3, v_2, v'_1
  47. Polygon(V', Z, B_1, C_1) → poly15, v'_2, v_3, b_4, c_2
  48. Polygon(R, Q, S, T) → poly16, r_3, q_2, s_2, t_3