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Cavalieri's Principle - Cone and Pyramid

Cavalieri's Principle - Cone and Pyramid
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2018-05-13 05:11
FunctionSolid GeometryGeometric Construction
This example demonstrates Cavalieri's principle, which states that if two solids have equal heights and the same cross-sectional area at every level, then they have the same volume. Key concepts include solid geometry, specifically cones and pyramids. The construction uses GeoGebra commands such as Plane, Pyramid, Circle, and Cone to create models of a cone and a pyramid. Suitable for high school geometry and solid geometry education.

GeoGebra Commands & Parameters

  1. Plane(A, xOyPlane) → a
  2. Pyramid(B, C, E, K, F) → b, face1, edge5, edge6, edge7, edge8, face2, face3, face4, face5, edge1, edge2, edge3, edge4
  3. Circle(D, 1.28379, xOyPlane) → e
  4. Cone(e, z(F) - z(C)) → j, j_2, j_3
  5. IntersectPath(a, j) → c
  6. IntersectPath(a, face3) → f
  7. Intersect(a, face3) → G, H
  8. IntersectPath(a, face4) → g
  9. Intersect(a, face4) → I, J
  10. IntersectPath(a, face2) → h
  11. Intersect(a, face2) → L, M
  12. Polygon(L, M, I, J) → q1, l, m, i, j_1