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Volume Experiment

Volume Experiment
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2017-09-11 04:41
Solid GeometryGeometric Construction
This example demonstrates how to explore volume changes through transformations of rectangles and cubes. Core math concepts include volume calculation, geometric properties of rectangles and cubes, and translation transformations. Construction highlights the use of GeoGebra commands and objects like Polygon, Translate, Prism, Segment, Angle, showcasing volume changes via slider animations. Suitable for high school solid geometry teaching and geometric construction learning.

GeoGebra Commands & Parameters

  1. Polygon(E, M, G) → poly2, f, g, k
  2. Polygon(B, A, C, D) → poly1, b, a, c, d
  3. Translate(A, v) → A'
  4. Translate(B, v) → B'
  5. Translate(C, v) → C'
  6. Translate(D, v) → D'
  7. Translate(E, v) → E'
  8. Translate(F, v) → F'
  9. Translate(G, v) → G'
  10. Prism(poly1, B') → h_1, H, edgeAH, edgeCI, edgeDJ, edgeB'H, edgeHI, edgeIJ, edgeB'J, I, J, faceABB'H, faceACIH, faceCDJI, faceBB'JD, faceB'HIJ, edgeBB'
  11. Prism(poly2, E') → i, K, edgeE'K, edgeKL, edgeE'L, L, faceEE'KF, faceFGLK, faceEE'LG, faceE'KL, edgeEE', edgeFK, edgeGL_1
  12. Segment(M, G) → j
  13. Angle(F, M, G) → α
  14. Polygon(G, M, F) → poly3, f_1, g_1, m
  15. Prism(poly3, L) → e, N, edgeLN, edgeNO, edgeLO, O, faceGLNM, faceFMNO, faceFGLO, faceLNO, edgeGL, edgeMN, edgeFO
  16. Segment(D, A) → l
  17. Segment(J, H) → n
  18. Angle(A, B, D) → β
  19. Angle(E, M, G) → γ
  20. Angle(D, C, A) → δ
  21. Segment(E, F) → p

AI Drawing Prompt Reference

Draw a cube and a rectangle, then use a slider to translate the rectangle vertically to form two rectangular prisms. Observe the volume changes. Connect the base of the cube to a prism formed by the rectangle and the side of the cube, and the top to a prism formed by the diagonal of the cube and the rectangle. Label the volumes of the rectangle, cube, and the three prisms, and display the three angles.
The prompt above was compiled from the original drawing commands and is for reference only.