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2013年AP考试第5c题：方柱体积

2013年AP考试第5c题：方柱体积
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2016-03-19 11:43
立体几何微积分积分
所属专题 AP Calculus volume problems
本示例演示了2013年AP考试第5c题，涉及立体几何中的方柱体积计算。通过使用GeoGebra命令如Polygon、Segment、Integral等，可以动态展示方柱的构造过程和体积变化。适合高中数学教学和学习，特别是微积分和立体几何相关课程。

GeoGebra 命令及参数

  1. Polygon(B, A, C, D) → Squares, a, c, d, b
  2. Segment(A, B) → e
  3. Angle(B, A, C) → α
  4. Locus(C, s) → loc1
  5. Integral((g(x) - f(x))^(2), 0, 2) → Integ
  6. If(togDF ≟ 1, "Show Instructions", "Show volume integral") → ToggleDirectionVolumeIntegral
  7. If(togS ≟ 1, "Hide surface", "Show surface") → ShowSurface
  8. Locus(D, s) → loc2
  9. Surface(u, (v * f(u)) + ((1 - v) * g(u)), 0, u, 0, 2, v, 0, 1) → Base
  10. Surface(u, g(u), (v * (g(u) - f(u))), v, 0, 1, u, 0, 2) → SurfaceBack
  11. Surface(u, f(u), (v * (g(u) - f(u))), v, 0, 1, u, 0, 2) → SurfaceFront
  12. Surface(u, (v * f(u)) + ((1 - v) * g(u)), g(u) - f(u), u, 0, 2, v, 0, 1) → Top
  13. Sequence(Polygon[((k * h), f(((k + p) * h)), 0), ((k * h), g(((k + p) * h)), 0), ((k * h), g(((k + p) * h)), ht(((k + p) * h))), ((k * h), f(((k + p) * h)), ht(((k + p) * h)))], k, 0, m - 1) → SlicesLeft
  14. Sequence(Polygon[(((k + 1) * h), f(((k + p) * h)), 0), (((k + 1) * h), g(((k + p) * h)), 0), (((k + 1) * h), g(((k + p) * h)), ht(((k + p) * h))), (((k + 1) * h), f(((k + p) * h)), ht(((k + p) * h)))], k, 0, m - 1) → SlicesRight
  15. Sequence(Surface[u, f(((k + p) * h)), (v * ht(((k + p) * h))), u, (k * h), ((k + 1) * h), v, 0, 1], k, 0, m - 1) → SlicesFront
  16. Sequence(Surface[u, g(((k + p) * h)), (v * ht(((k + p) * h))), u, (k * h), ((k + 1) * h), v, 0, 1], k, 0, m - 1) → SlicesBack
  17. Sequence(Surface[u, (v * f(((k + p) * h))) + ((1 - v) * g(((k + p) * h))), ht(((k + p) * h)), u, (k * h), ((k + 1) * h), v, 0, 1], k, 0, m - 1) → SlicesTop
  18. Sequence(Polygon[((k * h), f(((k + p) * h))), (((k + 1) * h), f(((k + p) * h))), (((k + 1) * h), g(((k + p) * h))), ((k * h), g(((k + p) * h)))], k, 0, m - 1) → SlicesBase
  19. Sequence(If[Defined[Area[Element[SlicesLeft, k]]], Area[Element[SlicesLeft, k]], 0], k, 1, m) → Areas