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Cylinder inside half-sphere

Cylinder inside half-sphere
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2016-01-08 07:14
Coordinate GeometrySolid GeometryGeometric Construction
This example demonstrates the geometric construction of a cylinder placed inside a unit hemisphere. Core math concepts include solid geometry, volume calculation, and spatial geometric relationships. It uses commands like RotateText, Surface, CurveCartesian, Circle, Cylinder, Mirror, Segment, Point in GeoGebra. Suitable for high school and university students learning spatial geometry construction and volume calculation.

GeoGebra Commands & Parameters

  1. RotateText("uStas\;\&\,Т.С.", 90°) → надпись01
  2. Surface(((R * sin(i)) * sin(j)), ((R * sin(i)) * cos(j)), zQ + (R * cos(i)), i, -1.5707963268, 1.5707963268, j, 0, 6.283185307179586) → Ω
  3. CurveCartesian((R * sin(j)), 0, zQ + (R * cos(j)), j, -1.5707963267948966, 1.5707963267948966) → ψ
  4. Circle(Q, R, zAxis) → ω
  5. Circle(O_1, r, xAxis) → φ_1
  6. Cylinder(φ_1, (-2 * h)) → d, φ_2, Φ
  7. Mirror(O_1, zAxis) → O_2
  8. Segment(O_1, O_2) → b
  9. Point(ω, 0.5) → A_1
  10. Point(ω, 0) → A_2
  11. Segment(A_1, A_2) → c
  12. Point(φ_1, 0.75) → B_1
  13. Mirror(B_1, zAxis) → B_2
  14. Point(φ_1, 0.25) → C_1
  15. Mirror(C_1, zAxis) → C_2
  16. Segment(B_1, C_1) → a_1
  17. Segment(B_2, C_2) → a_2
  18. Segment(Q, B_1) → a
  19. Segment(B_1, B_2) → e