圆柱体体积计算演示 by Lenore Horner

几何画板及绘图内容加载中，请稍等……

2020-01-09 07:42

①本范例演示如何通过多个圆柱体组合或分解来计算复杂几何体的体积；②涉及核心数学概念包括微积分中的积分、立体几何中的体积计算、二次方程求解以及优化问题；③作图要点使用了Point, Segment, Textfield, Surface, If, CurveCartesian, LaTeX等GeoGebra命令和对象，如通过滑块调整参数、绘制函数图像、计算交点等；④适合高中及以上学生学习微积分、立体几何以及体积计算方法，也可用于概率统计中的几何概率演示。

GeoGebra 命令及参数

Point(xAxis) → Left
Point(xAxis) → Right
Point(f) → A
Segment(B, A) → a
Textfield(g) → inputBox1
Textfield(h) → inputBox2
Segment((x(Left), g(x(Left))), (x(Left), h(x(Left)))) → j
Segment((x(Right), g(x(Right))), (x(Right), h(x(Right)))) → l
Surface((x(A) * cos((-t))), u, (x(A) * sin((-t))), t, 0, β, u, Min[y(A), y(B)], Max[y(A), y(B)]) → d
If(α > 0, Surface[(u * cos((-t))), g(u), (u * sin((-t))), t, 0, α, u, x(Left), x(Right)]) → e
Surface((u * cos((-t))), k(u), (u * sin((-t))), t, 0, α, u, x(Left), x(Right)) → i
Surface((x(Left) * cos((-t))), u, (x(Left) * sin((-t))), t, 0, α, u, Min[g(x(Left)), h(x(Left))], Max[g(x(Left)), h(x(Left))]) → m
Surface((x(Right) * cos((-t))), u, (x(Right) * sin((-t))), t, 0, α, u, Min[g(x(Right)), h(x(Right))], Max[g(x(Right)), h(x(Right))]) → n
CurveCartesian((x(A) * cos((-t))), y(A), (x(A) * sin((-t))), t, 0, α) → b
CurveCartesian((x(A) * cos((-t))), y(B), (x(A) * sin((-t))), t, 0, α) → c
LaTeX((((("\text{V}=2\pi\int_{x_{\text{Left}}}^{x_{\text{Right}}}x\left[\left(" * g) * "\right)-\left(") * h) * "\right)\right] dx")) → text1