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Sphere Inside a Half Pyramid

Sphere Inside a Half Pyramid
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2015-10-29 23:58
TrigonometrySolid GeometryGeometric Construction
This example demonstrates the geometric relationship and properties of a sphere inscribed within a half pyramid. Key math concepts include solid geometry, volume calculation, trigonometric function applications, and geometric construction. The construction uses GeoGebra commands like Pyramid, PointIn, Point, and Sphere. It is suitable for high school students and math enthusiasts to understand spatial geometry and volume calculations, serving as a teaching demonstration or exploration tool.

GeoGebra Commands & Parameters

  1. Pyramid(A, B, C, D, (7.682550981176465, 3.6214647018836707, 0)) → a, faceABCD, edge1, edge2, edge3, edge4, face1, face3, face4, face2, edgeAB, edgeBC, edgeCD, edgeAD
  2. PointIn(face2) → F
  3. Point(edge4) → G
  4. Sphere(F, G) → b

AI Drawing Prompt Reference

Draw a half pyramid with a quadrilateral base and an apex above the center of the base. Inside the half pyramid, draw a sphere such that its center lies on the line connecting the midpoint of one base edge and the apex, and the sphere is tangent to the pyramid's lateral faces.
The prompt above was compiled from the original drawing commands and is for reference only.