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Cross section of various solids: Exploring planar sections of 3D shapes

Cross section of various solids: Exploring planar sections of 3D shapes
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2019-04-15 05:48
Solid GeometryGeometric ConstructionLocus
This example demonstrates the analysis of cross-sections of various solids using GeoGebra. Key mathematical concepts include the relationship between planes and solids, derivation of cross-section shapes, and spatial geometry visualization. Construction involves using commands like IndexOf, Point, Cube, Pyramid, Cylinder, Cone, and IntersectPath to create objects and calculate sections. Suitable for high school students or college freshmen to learn solid geometry and spatial reasoning.

GeoGebra Commands & Parameters

  1. IndexOf(SelectedElement[l1], l1) → a
  2. Point(Circle[(3, -3, -3), Distance[(-3, -3, -3), (3, -3, -3)], Segment[(-3, -3, -3), (3, -3, -3)]]) → A
  3. Cube((-3, -3, -3), (3, -3, -3), A) → b, B, faceABFE, faceCDEF, edge2, edge1, edge4, edgeAB, edge3, edgeBF, edgeCF, edgeCD, C, edge5, edgeDE, edgeAE, edgeEF, D, E, F, face1, face3, face2, face4
  4. Pyramid(face1, (0, 0, 3)) → c, face6, face5, face7, face8, edge9, edge6, edge7, edge8
  5. Cylinder((0, 0, -3), (0, 0, 3), 3) → d, e, f, g
  6. Cone((0, 0, -3), (0, 0, 3), 3) → h, k, i
  7. Translate(Rotate[z = 0, tilt, xAxis], Vector[(0, 0, UpDown)]) → j
  8. IntersectPath(j, b) → poly1, G, H, I, J, l, m, n, p
  9. IntersectPath(j, d) → q
  10. Corner(q) → K, L, M, N
  11. IntersectPath(j, c) → poly2, O, P, Q, R, r, s, t, f_1
  12. IntersectPath(j, h) → c_1
  13. Corner(c_1) → S, T, U, V

AI Drawing Prompt Reference

Draw a 3D solid consisting of a cube, a pyramid, a cylinder, and a cone, and show their intersection with an inclined plane. The drawing should include the faces of the cube, the apex of the pyramid, the sides of the cylinder and cone, and the polygonal cross-section. The construction should start with the basic solids, then add the inclined plane, and finally calculate the intersection.
The prompt above was compiled from the original drawing commands and is for reference only.