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Spatial Geometry Cross-Section Visualization

Spatial Geometry Cross-Section Visualization
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2016-06-16 07:57
Coordinate GeometrySolid GeometryGeometric Construction
This example demonstrates how to visualize cross-sections of spheres, cones, and cylinders by intersecting them with planes, showcasing the resulting shapes. Key math concepts include solid geometry, cross-sectional geometry, and volume calculations. Construction highlights the use of GeoGebra commands/objects like Circle, Cylinder, Cone, Sphere, OrthogonalPlane, IntersectPath, Corner, Point, Rotate, and Plane. Suitable for high school and above students to learn about spatial geometric solids and their cross-section properties.

GeoGebra Commands & Parameters

  1. Circle(zAxis, A) → c
  2. Cylinder(c, 4) → a, d, b
  3. Circle(zAxis, A) → f
  4. Cone(f, 4) → g, h, i
  5. Sphere((0, 0, 0), 2) → k
  6. OrthogonalPlane(B, zAxis) → n
  7. IntersectPath(n, a) → p
  8. IntersectPath(n, g) → q
  9. IntersectPath(n, k) → r
  10. OrthogonalPlane(C, yAxis) → s
  11. IntersectPath(s, a) → c_1
  12. Corner(c_1) → D, E, F, G
  13. IntersectPath(s, g) → d_1
  14. Corner(d_1) → H, I, J, K
  15. IntersectPath(s, k) → e_1
  16. Point(zAxis) → L
  17. Rotate(M, 90°, zAxis) → M'
  18. Plane(M', M, L) → v
  19. IntersectPath(v, a) → f_1
  20. Corner(f_1) → N, O, P, Q
  21. IntersectPath(v, g) → g_1
  22. Corner(g_1) → R, S, T, U
  23. IntersectPath(v, k) → h_1