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Oblique and Right Pyramid - Cavalieri's Principle

Oblique and Right Pyramid - Cavalieri's Principle
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2014-09-26 02:06
Solid GeometryCalculusGeometric Construction
In collections Area, Surface Area, Volume, Cross Section, 3D
This example demonstrates Cavalieri's Principle applied to pyramids, exploring the volume relationship between oblique and right pyramids with identical bases and heights by adjusting apex positions. Key math concepts include Cavalieri's Principle, pyramid volume, and 3D geometry. Construction highlights Polygon, Pyramid, Intersect, and IntersectPath commands in GeoGebra. Ideal for high school solid geometry instruction to visually grasp the principle.

GeoGebra Commands & Parameters

  1. Polygon((0, 0), (0, 1), (1, 1), (1, 0)) → poly1, a, b, c, d
  2. Pyramid(poly1, A) → e, face1, face3, face4, face2, edge1, edge2, edge3, edge4
  3. Polygon((0, 0), B, C, D) → poly2, g, b_1, c_1, d_1
  4. Pyramid(poly2, E) → h, face5, faceBCE, faceCDE, face6, edge5, edgeBE, edgeCE, edgeDE
  5. Intersect(edge1, f) → F
  6. Intersect(edge4, f) → G
  7. Intersect(edge2, f) → H
  8. Intersect(edge3, f) → I
  9. Intersect(edgeBE, f) → J
  10. Intersect(edgeCE, f) → K
  11. Intersect(edgeDE, f) → L
  12. Intersect(edge5, f) → M
  13. IntersectPath(f, e) → poly3, poly5, A_1, F_1, i, j, k, l, r, t, a_1, e_1, poly7, j_1, N, O, P, Q, V, W, Z
  14. IntersectPath(f, h) → poly4, poly6, E_1, G_1, m, n, p, q, f_1, g_1, h_1, i_1, poly8, k_1, R, S, T, U, B_1, C_1, D_1

AI Drawing Prompt Reference

Draw a right pyramid and an oblique pyramid with the same base area and height, showing the intersection lines of their lateral faces with a plane to verify Cavalieri's Principle, highlighting the shapes formed by these intersections.
The prompt above was compiled from the original drawing commands and is for reference only.