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两圆柱相交的体积

两圆柱相交的体积
几何画板及绘图内容加载中，请稍等……
2015-07-16 22:46
立体几何
所属专题 intersection: surface-surface, curve-curve intersection: surface-surface, curve-curve intersection: surface-surface, curve-curve intersection: surface-surface, curve-curve Volumes in Calculus Volumes in Calculus
该范例演示了半径为2的两圆柱相交的体积。核心数学概念包括立体几何中的体积计算。通过使用GeoGebra命令如Cylinder, IntersectPath, Point等，可以构造出相交圆柱的几何图形。适合高中或大学的立体几何学习。

GeoGebra 命令及参数

  1. Cylinder((4, 0, 0), (-4, 0, 0), 2) → a, c, d, b
  2. Cylinder((0, -4, 0), (0, 4, 0), 2) → e, f, g, h
  3. IntersectPath(plane1, e) → k
  4. Point(k) → A
  5. Conic((2, 2, 0), (-2, -2, 0), (0, 0, 2), (0, 0, -2), (1.4142135623730951, 1.4142135623730951, 1.4142135623730951)) → p
  6. IntersectPath(plane2, a) → q
  7. CurveCartesian((2 * cos(t)), (2 * cos(t)), (2 * sin(t)), t, 0, 6.28319) → crv1
  8. CurveCartesian((2 * cos(t)), (-2 * cos(t)), (2 * sin(t)), t, 0, 6.28319) → crv2
  9. Surface(u, v / ((-u) ≤ v ≤ u), sqrt(4 - u^(2)), u, -2, 2, v, -2, 2) → SecTop1
  10. Surface((-u), v / ((-u) ≤ v ≤ u), sqrt(4 - u^(2)), u, -2, 2, v, -2, 2) → SecTop3
  11. Surface(u / ((-v) ≤ u ≤ v), (-v), sqrt(4 - v^(2)), u, -2, 2, v, -2, 2) → SecTop2
  12. Surface(u / ((-v) ≤ u ≤ v), v, sqrt(4 - v^(2)), u, -2, 2, v, -2, 2) → SecTop4
  13. Surface(u, v / ((-u) ≤ v ≤ u), (-sqrt(4 - u^(2))), u, -2, 2, v, -2, 2) → SecBottom1
  14. Surface(u, (-u), v / ((-sqrt(4 - u^(2))) ≤ v ≤ sqrt(4 - u^(2))), u, 0, 2, v, -2, 2) → SectSide1_1
  15. Surface(u, u, v / ((-sqrt(4 - u^(2))) ≤ v ≤ sqrt(4 - u^(2))), u, 0, 2, v, -2, 2) → SectSide1_2
  16. Surface((-u), u, v / ((-sqrt(4 - u^(2))) ≤ v ≤ sqrt(4 - u^(2))), u, 0, 2, v, -2, 2) → SecSide3_1
  17. Surface(u / ((-v) ≤ u ≤ v), (-v), (-sqrt(4 - v^(2))), u, -2, 2, v, -2, 2) → SecBottom2
  18. Surface(u, u, v / ((-sqrt(4 - u^(2))) ≤ v ≤ sqrt(4 - u^(2))), u, -2, 0, v, -2, 2) → SecSide2_1
  19. Surface((-u), v / ((-u) ≤ v ≤ u), (-sqrt(4 - u^(2))), u, -2, 2, v, -2, 2) → SecBottom3
  20. Surface(u / ((-v) ≤ u ≤ v), v, (-sqrt(4 - v^(2))), u, -2, 2, v, -2, 2) → SecBottom4
  21. Polygon((ss, ss, PlaneHeight), ((-ss), ss, PlaneHeight), ((-ss), (-ss), PlaneHeight), (ss, (-ss), PlaneHeight)) → Square, i, j, l, m