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Revolution of Area Between Curves Around x-axis

Revolution of Area Between Curves Around x-axis
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2015-02-02 01:47
FunctionSolid GeometryCalculusIntegralGraphing
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This example demonstrates revolving a region bounded by two functions around the x-axis to form a solid of revolution. Key math concepts include integral calculus, volume of solids of revolution, and function graphing in coordinate geometry. Constructed using GeoGebra commands like Textfield, Surface, and Sequence. Suitable for high school and above students to learn about volume calculations and geometric properties of function graphs.

GeoGebra Commands & Parameters

  1. Textfield(f_1) → inputBox1
  2. Surface(k, (f_1(k) * cos(A)), (f_1(k) * sin(A)), k, a, b, A, 0.01, α) → c
  3. Surface(k, (g(k) * cos(A)), (g(k) * sin(A)), k, a, b, A, 0.01, α) → d
  4. Textfield(g) → inputBox2
  5. Sequence(Segment[(a + ((b - a) / N * n), (f_1(a + ((b - a) / N * n)) * cos(α)), (f_1(a + ((b - a) / N * n)) * sin(α))), (a + ((b - a) / N * n), (g(a + ((b - a) / N * n)) * cos(α)), (g(a + ((b - a) / N * n)) * sin(α)))], n, 1, N) → list1
  6. Surface(p, (k * cos(α)), (k * sin(α)), p, a, b, k, g(p), f_1(p)) → e
  7. Surface(b, (r * cos(p)), (r * sin(p)), p, 0, 6.283185307179586, r, g(b), f_1(b)) → f
  8. Surface(a, (r * cos(p)), (r * sin(p)), p, 0, 6.28319, r, g(a), f_1(a)) → i