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Shell Method Volume Graphic

Shell Method Volume Graphic
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2016-02-04 02:19
Solid GeometryCalculusIntegral
This example provides a simple graphic to illustrate how to calculate volumes of solids of revolution using the shell method. It involves integral calculus, rotation of shapes, and the shell method technique. Constructed with GeoGebra commands like Textfield, CurveCartesian, Segment, Circle, Surface, etc. Ideal for high school and above students learning volume calculations in calculus.

GeoGebra Commands & Parameters

  1. Textfield(a) → inputa
  2. Textfield(b) → inputb
  3. Textfield(f1) → inputf
  4. CurveCartesian(posit, t, 0, t, 0, f(posit)) → curve1
  5. Segment((b, 0, 0), (b, f(b), 0)) → bline
  6. Circle((0, 0, 0), posit, Plane[(0, 0, 0), (1, 0, 0), (0, 0, 1)]) → c
  7. Segment((a, 0, 0), (a, f(a), 0)) → aline
  8. Circle((0, f(posit), 0), posit, Plane[(0, 0, 0), (1, 0, 0), (0, 0, 1)]) → d
  9. Surface((posit * cos(t2)), t1, (posit * sin(t2)), t1, 0, f(posit), t2, 0, (2 * π)) → shell
  10. Surface((min * cos(t)), (u * f(min)), (min * sin(t)), t, 0, (2 * π), u, 0, 1) → hole
  11. Surface((max * cos(t)), (u * f(max)), (max * sin(t)), t, 0, (2 * π), u, 0, 1) → case
  12. Surface((u * cos(t)), 0, (u * sin(t)), t, 0, (2 * π), u, min, max) → washer
  13. Surface((u * cos(t)), f(u), (u * sin(t)), t, 0, (2 * π), u, min, max) → top