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Pyramid Volume and Cross Section

Pyramid Volume and Cross Section
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2017-05-18 22:28
Coordinate GeometrySolid GeometryGeometric Construction
This example demonstrates the calculation of a pyramid's volume using cross-sections. Key concepts include the volume formula for a pyramid and the cross-section method. It utilizes GeoGebra commands and objects such as points, segments, polygons, and pyramids. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  1. Corner(2) → C2
  2. Corner(1) → C1
  3. Segment((0.95 * C1) + (0.05 * C2) + (0, (1 / 4 * height)), (0.95 * C1) + (0.05 * C2) + (0, (3 / 4 * height))) → j
  4. Point(j) → O
  5. First(list1, N) → list2
  6. Polygon(list2) → poly1
  7. Pyramid(poly1, (x(P), y(P), ht)) → a, face1, edge5, face2, face3, face4, face5, edge1, edge2, edge3, edge4
  8. Point(Segment[M, O]) → Q
  9. IntersectPath(z = c, a) → poly2, I, l, J, K, L, R, f, g, h, i
  10. Segment(P, P + (0, 0, ht)) → k