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Volumes of Revolution by Andy Cooper

Volumes of Revolution by Andy Cooper
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2015-12-10 16:34
Solid GeometryCalculusIntegral
This example demonstrates the calculation of volumes of revolution. Key mathematical concepts include integration and geometric transformations. Using GeoGebra commands such as Point, Arc, Segment, and Vector, the cross-sections and arcs of the revolution body are constructed, and the volume is calculated. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  1. Point(f) → A
  2. OrthogonalLine(A, xAxis) → a
  3. Point(f) → B
  4. OrthogonalLine(B, xAxis) → c
  5. Intersect(c, xAxis) → B'
  6. Intersect(f', a, 1) → E
  7. Arc(e, A, E) → h
  8. Arc(e, E, A) → k
  9. Intersect(f', c, 1) → F
  10. Arc(d, B, F) → p
  11. Arc(d, F, B) → q
  12. Point(f) → C
  13. OrthogonalLine(C, xAxis) → i
  14. Intersect(f', i, 1) → H
  15. Intersect(i, xAxis) → I
  16. Segment(C, J) → height_1
  17. Segment(K, H) → height_2
  18. Arc(E_1, C, H) → Arc_{1a}
  19. Arc(E_1, H, C) → Arc_{1b}
  20. Arc(E_2, J, K) → Arc_{2a}
  21. Arc(E_2, K, J) → Arc_{2b}
  22. Intersect(a, xAxis) → A'
  23. Sequence((x - x(A) - (k * a_1))^(2) / b^(2) + y^(2) = f(x(A) + (k * a_1))^(2), k, 1, n) → partition
  24. Point(height_1) → M
  25. Vector(L, M) → u
  26. Point(xAxis) → D