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Cross Section Solid Example: Squares

Cross Section Solid Example: Squares
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2019-03-06 19:32
Solid GeometryCalculusIntegralGeometric Construction
This example demonstrates how to calculate the 3D solid generated by rotating a square through integration. Key math concepts include Calculus, Integral Calculus, Solid Geometry, Piecewise Functions, Upper and Lower Sum or Riemann Sum, and Fractal Geometry. Construction highlights involve using GeoGebra commands like CurveCartesian, Polygon, and Surface with objects f, g, a, b, n, q1, h, i, j, k, c, d, e. Suitable for high school and above students learning complex geometric constructions and calculus applications.

GeoGebra Commands & Parameters

  1. CurveCartesian(t, f(t), f(t) - g(t), t, 0, 2) → a
  2. CurveCartesian(t, g(t), f(t) - g(t), t, 0, 2) → b
  3. Polygon((n, g(n), 0), (n, f(n), 0), a(n), b(n)) → q1, h, i, j, k
  4. Surface(t, g(t), (u * z(b(t))), t, 0, 2, u, 0, 1) → c
  5. Surface(t, f(t), (u * z(a(t))), t, 0, 2, u, 0, 1) → d
  6. Surface(t, (u * g(t)) + ((1 - u) * f(t)), z(a(t)), t, 0, 2, u, 0, 1) → e