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Volume of Solids of Revolution by Juan Carlos Ponce Campuzano

Volume of Solids of Revolution by Juan Carlos Ponce Campuzano
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2018-12-11 19:08
FunctionSolid GeometryCalculusIntegral
This example demonstrates the process of generating a solid of revolution by rotating a 2D region and calculating its volume. Key math concepts include integration, function graphing, geometric transformations, and volume computation. GeoGebra commands and objects used in construction are Sequence, Sum, RectangleSum, Integral, Textfield, Surface, and If. Suitable for high school and above students to understand volume calculation methods and calculus applications.

GeoGebra Commands & Parameters

  1. Sequence(Cylinder[(ax + (deltax * k / n), 0), (ax + (deltax * (k + 1) / n), 0), f((ax + (deltax * k / n) + ax + (deltax * (k + 1) / n)) / 2)], k, 0, n - 1) → list1
  2. Sum(list1) → appsum
  3. RectangleSum(f, ax, bx, n, 0.5) → a
  4. Integral((π * f(x)^(2)), ax, bx) → actualsum
  5. Textfield(f) → InputBox1
  6. Textfield(ax) → InputBox2
  7. Textfield(bx) → InputBox3
  8. Surface(t, (f(t) * cos(u)), (f(t) * sin(u)), t, ax, bx, u, 0, rot) → b
  9. If(f(ax) ≟ f(ax), 1, 0) → conda
  10. If(f(bx) ≟ f(bx), 1, 0) → condb