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Volume of a Cone Demo

Volume of a Cone Demo
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2015-11-05 03:00
TrigonometrySolid GeometryGeometric Construction
This example demonstrates the calculation and geometric properties of a cone's volume. It involves core math concepts like solid geometry, cone volume formula, and rotational solids. Construction highlights include commands like Circle, Segment, Rotate, Intersect, CircleSector, Cone, Mirror, Sequence, and Angle in GeoGebra. Suitable for high school students and math enthusiasts to understand the cone volume formula and 3D shape construction.

GeoGebra Commands & Parameters

  1. Circle((0, 0), P) → c
  2. Circle((0, 0), 2) → d
  3. Segment((0, 0), (0, 2)) → b
  4. Rotate(b, (-α), (0, 0)) → b'
  5. Intersect(d, b, 1) → A
  6. Intersect(d, b', 1) → B
  7. CircleSector((0, 0), A, B) → e
  8. Segment((0, 0, 0), S) → f
  9. Cone(c, f) → g, h, i
  10. Mirror(g, xOyPlane) → g'
  11. Mirror(i, xOyPlane) → i'
  12. Mirror(S, xOyPlane) → S'
  13. Segment(S', P) → j
  14. Sequence(Segment[Rotate[S', (π * n / 12), zAxis], Rotate[P, (π * n / 24), zAxis]], n, 0, 60) → list1
  15. Angle(b', b) → β
  16. Mirror(S', zAxis) → S''
  17. Mirror(P, zAxis) → P'
  18. Segment(S'', P') → j'
  19. Angle(j, j') → γ