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Volume of Solid of Revolution (About the x-Axis)

Volume of Solid of Revolution (About the x-Axis)
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2017-05-16 08:06
FunctionSolid GeometryCalculusIntegralGeometric Construction
This example demonstrates the calculation of the volume of a solid formed by revolving a function around the x-axis. Key math concepts include solid of revolution and integral applications in calculus. Construction highlights the use of GeoGebra commands like Sequence, Point, Ellipse, Segment, CircleArc, and Vector. Suitable for high school students and above learning calculus and solid geometry, or for educational purposes.

GeoGebra Commands & Parameters

  1. Sequence((i, i^(0.5)), i, 0, a, 0.25) → list1
  2. Sequence((i, (-i^(0.5))), i, 0, a, 0.25) → list2
  3. Sequence(Segment[Element[list1, i], Element[list2, i]], i, 0, a) → list3
  4. Sequence((i + b, 0), i, 0, a, 0.25) → list5
  5. Sequence(Ellipse[Element[list1, i], Element[list2, i], Element[list5, i]], i, 0, a, 0.25) → list4
  6. Sequence(Point[Element[list4, i], c], i, 0, (10 * a)) → list6
  7. Point(i) → D
  8. Point(h) → E
  9. Point(i) → F
  10. Point(h) → G
  11. Point(j) → H
  12. Ellipse(D, E, H) → e
  13. Point(j) → I
  14. Ellipse(F, G, I) → k_1
  15. Segment(J, F) → l
  16. Segment(G, K) → m
  17. Point(j) → L
  18. CircleArc(L, F, G) → k
  19. Segment(M, N) → p
  20. Point(p) → O
  21. Vector(O, P) → u