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Cone Frustum Demonstration

Cone Frustum Demonstration
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2020-04-29 21:58
Solid GeometryGeometric ConstructionGraphing
This example demonstrates the geometric construction and visualization of a cone frustum. It involves core mathematical concepts such as solid geometry, volume calculation, and surface area formulas. Key GeoGebra commands used include Circle, Segment, Translate, Cone, and Surface. Suitable for high school students and mathematics enthusiasts learning about three-dimensional geometry and spatial figures.

GeoGebra Commands & Parameters

  1. Circle(C, R, xOyPlane) → c
  2. Segment(P, C) → f
  3. Circle(P, r, xOyPlane) → d
  4. Segment(C, C') → l
  5. Segment(P, P') → m
  6. Segment(P', C') → n
  7. Translate(P, Vector[(t * u)]) → P'_2
  8. Translate(P', Vector[(t * u)]) → P''
  9. Segment(P'_2, P'') → m'
  10. Cone(C, A, R) → a, e, b
  11. Segment(A, C) → i
  12. Segment(A, C') → j
  13. Cone(P, A, r) → k, p, q
  14. Segment(A, P) → s
  15. Segment(A, P') → f_1
  16. Surface(((r + ((1 / H * (H - z)) * (R - r))) * cos(t)), ((r + ((1 / H * (H - z)) * (R - r))) * sin(t)), z, z, 0, H, t, 0, (2 * pi)) → b_1
  17. Translate(A, Vector[(t * u)]) → A'_{1}
  18. Segment(A'_{1}, P'_2) → g_1
  19. Segment(P'', A'_{1}) → h_1
  20. Translate(q, Vector[(t * u)]) → q'
  21. Translate(p, Vector[(t * u)]) → p'