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Volume by Cylindrical Shell

Volume by Cylindrical Shell
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2018-12-16 09:24
FunctionCalculusIntegral
This example demonstrates the calculation of the volume of a solid formed by rotating a function around an axis using the cylindrical shell method. Key math concepts include integration, limits, and function graph rotation. Construction highlights involve GeoGebra commands like Sequence, Line, Rotate, Polygon, Distance, Point, Segment, and Textfield. Suitable for high school and above students learning calculus volume methods and geometric visualization.

GeoGebra Commands & Parameters

  1. Sequence((a + (i * deltax), 0), i, 1, n) → list1
  2. Sequence(x(Element[list1, i]), i, 1, n) → xcoords
  3. Sequence(f(Element[xcoords, i]), i, 1, n) → list2
  4. Sequence((Element[xcoords, i], Element[list2, i]), i, 1, n) → pointsoncurve
  5. Sequence((Element[xcoords, i], Element[list2, i + 1]), i, 1, n) → list3
  6. Sequence(Polygon[Element[list1, i], Element[list3, i], Element[pointsoncurve, i + 1], Element[list1, i + 1]], i, 1, n) → rectangles
  7. Line((w, 0, 0), (w, 1, 0)) → g
  8. Rotate(A, α, g) → A'
  9. Rotate(B, α, g) → B'
  10. Rotate(C, α, g) → C'
  11. Rotate(D, α, g) → D'
  12. Polygon(A', B', C', D') → poly1', a', b', c', d'
  13. Distance(g, c) → d_1
  14. Point(g) → E
  15. Sequence(Rotate[poly1', β, g], β, 1°, 359°, 1°) → firstshell
  16. Sequence(Rotate[rectangles, β, g], β, 1°, 360°, 1°) → shells
  17. Segment(B', C') → j
  18. Sequence(Rotate[list3, β, g], β, 1°, 360°, 1°) → circles
  19. Textfield(f) → InputBox1