圆底等腰直角三角形横截面的立体图形

几何画板及绘图内容加载中，请稍等……

2015-07-02 12:38

所属专题 intersection: surface-surface, curve-curve intersection: surface-surface, curve-curve intersection: surface-surface, curve-curve intersection: surface-surface, curve-curve BC Calculus Volumes in Calculus Volumes in Calculus

该范例演示了一个以圆为底面的立体图形，其横截面为等腰直角三角形，且直角边位于底面。涉及的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Circle, Polygon, Locus, Integral等，可以构造出该立体图形。适合高中数学教学或学习立体几何体积计算。

GeoGebra 命令及参数

Circle((0, 0), 3) → c
Polygon(C, B, A) → poly1, a_1, c_1, b_1
Locus(C, s) → loc1
Integral(9 - x^(2), -3, 3) → VolInt
If(togV ≟ 0, "Show volume integral", "Hide volume integral") → ShowVolInteg
If(togD ≟ 1, "Hide description", "Show description") → ShowDescrip
Surface(u, v / ((-f(u)) ≤ v ≤ f(u)), 0, v, -3, 3, u, -3, 3) → Base
If(togS ≟ 1, "Hide surface", "Show surface") → ShowSurface
Angle(A, C, B) → α
Surface(u, (v * f(u)), f(u) - (v * f(u)), u, -3, 3, v, 0, 1) → SurfaceFront
Surface(u, ((-v) * f(u)), f(u) - (v * f(u)), u, -3, 3, v, 0, 1) → SurfaceBack
Sequence(Polygon[(-3 + (k * h), f(-3 + ((k + p) * h)), 0), (-3 + (k * h), (-f(-3 + ((k + p) * h))), 0), (-3 + ((k + 1) * h), (-f(-3 + ((k + p) * h))), 0), (-3 + ((k + 1) * h), f(-3 + ((k + p) * h)), 0)], k, 0, m - 1) → SlicesBase
Sequence(Polygon[(-3 + (k * h), f(-3 + ((k + p) * h)), 0), (-3 + (k * h), (-f(-3 + ((k + p) * h))), 0), (-3 + (k * h), 0, f(-3 + ((k + p) * h)))], k, 0, m - 1) → SidesLeft
Sequence(Polygon[(-3 + ((k + 1) * h), f(-3 + ((k + p) * h)), 0), (-3 + ((k + 1) * h), (-f(-3 + ((k + p) * h))), 0), (-3 + ((k + 1) * h), 0, f(-3 + ((k + p) * h)))], k, 0, m - 1) → SidesRight
Sequence(Surface[-3 + ((k + u) * h), ((v - 1) * f(-3 + ((k + p) * h))), (v * f(-3 + ((k + p) * h))), u, 0, 1, v, 0, 1], k, 0, m - 1) → SlicesFront
Sequence(Surface[-3 + ((k + u) * h), ((1 - v) * f(-3 + ((k + p) * h))), (v * f(-3 + ((k + p) * h))), u, 0, 1, v, 0, 1], k, 0, m - 1) → SlicesBack
Sequence(Area[Element[SidesLeft, k]], k, 1, m) → Areas