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Investigating Volume

Investigating Volume
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2017-04-22 22:51
VectorSolid GeometryCalculus
This example uses GeoGebra to explore the concept of volume. Key mathematical concepts include 3D vectors, similarity transformations, and integral calculus. Using commands like Vector, Line, Intersect, Segment, Polygon, and Midpoint, the example constructs length, height, width, and other objects to demonstrate how to calculate the volume of geometric shapes. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  1. Vector(((0.75 * width), (0.5 * width))) → w
  2. Vector((0, height)) → z
  3. Vector(((-0.75 * length), (0.4 * length))) → u
  4. Line(C, z) → d
  5. Line(B, w) → e
  6. Line(B, u) → f
  7. Line(A, z) → g
  8. Intersect(f, g) → D
  9. Intersect(d, e) → E
  10. Segment(A, D) → h
  11. Segment(D, B) → i
  12. Segment(B, E) → j
  13. Segment(E, C) → k
  14. Line(D, j) → l
  15. Line(E, i) → m
  16. Intersect(l, m) → F
  17. Segment(D, F) → n
  18. Segment(F, E) → p
  19. Polygon(D, A, O, B) → poly1, d_1, a_1, o, b_1
  20. Polygon(D, F, E, B) → poly2, d_2, f_1, e_1, b_2
  21. Polygon(O, C, E, B) → poly3, o_1, c_1, e_2, b_3
  22. Midpoint(o_1) → G
  23. Midpoint(c_1) → H
  24. Midpoint(a_1) → I