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Volume of Solid of Revolution by Belinda Elliott

Volume of Solid of Revolution by Belinda Elliott
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2017-02-11 12:44
FunctionSolid GeometryIntegral
This example demonstrates the calculation of the volume of a solid of revolution. Key mathematical concepts include functions, integration, and solid geometry. Using GeoGebra commands such as Surface, Intersect, and Segment, the construction of the solid and its volume calculation can be achieved. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  1. Surface(t, (f(t) * cos(A)), (f(t) * sin(A)), t, 0, 4, A, 0, α) → a
  2. Surface((g(t) * cos(A)), t, (g(t) * sin(A)), t, 0, 4, A, 0, α) → b
  3. Surface((g(t) * cos(A)), t, (g(t) * sin(A)), t, s, s + 0.1, A, 0, α) → c
  4. Surface((g(r) * cos(A)), s, (g(r) * sin(A)), r, 0, s, A, 0, α) → d
  5. Intersect(f, e, 1) → A
  6. Intersect(f, e, 2) → B
  7. Segment(A, B) → i
  8. Segment(A, B) → j
  9. Distance(A, B) → AB
  10. Segment(P, Q) → k
  11. Surface((t * cos(T)), s, (t * sin(T)), t, x(A), x(B), T, 0, 360°) → l
  12. Surface((h(t) * cos(A)), t, (h(t) * sin(A)), t, 0, 4, A, 0, α) → m
  13. Surface((g(t) * cos(A)), t, (g(t) * sin(A)), t, 0, 4, A, 0, α) → n

AI Drawing Prompt Reference

Draw a solid of revolution to demonstrate the calculation of volume, showing the surface formed by rotating a function around an axis, including the line connecting the intersection points of two function graphs, and the surface and cross-section of the solid, suitable for high school mathematics education.
The prompt above was compiled from the original drawing commands and is for reference only.