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Volume of a Prism by Accesscd

Volume of a Prism by Accesscd
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2013-05-23 02:52
Solid GeometryGeometric ConstructionSlider Animation
In collections Area and Volume
This example demonstrates the calculation of the volume of a prism. It involves core mathematical concepts such as area, volume, hypothesis testing, statistics, square, logarithmic functions, and power functions. The construction uses commands like Point, Segment, Rotate, Line, OrthogonalLine, Intersect, and Polygon. It is suitable for high school mathematics teaching and learning about volume calculations.

GeoGebra Commands & Parameters

  1. Point(Circle[A, l]) → B
  2. Segment(A, B) → length
  3. Point(Circle[A, w]) → C
  4. Segment(A, C) → b
  5. Rotate(A, 30*°, A) → A'
  6. Rotate(C, 30*°, A) → C'
  7. Segment(A', C') → b'
  8. Point(Circle[A, h]) → D
  9. Segment(A, D) → c
  10. Rotate(A, 90*°, A) → A'_1
  11. Rotate(D, 90*°, A) → D'
  12. Segment(A'_1, D') → height
  13. Line(D', A) → d
  14. OrthogonalLine(D', height) → e
  15. OrthogonalLine(B, length) → f
  16. Line(C', length) → g
  17. Line(B, b') → i
  18. Intersect(d, height) → E
  19. Intersect(e, f) → F
  20. Intersect(i, g) → G
  21. Segment(C', G) → j
  22. Segment(B, G) → width
  23. Segment(D', F) → m
  24. Segment(F, B) → n
  25. Line(F, width) → p
  26. Line(D', b') → q
  27. Line(C', height) → r
  28. Line(G, n) → s
  29. Intersect(q, r) → H
  30. Intersect(s, p) → I
  31. Segment(D', H) → t
  32. Segment(H, I) → a_1
  33. Segment(F, I) → b_1
  34. Segment(I, G) → c_1
  35. Segment(H, C') → d_1
  36. Polygon(C', A, B, G) → poly1, c', a, b_2, g_1

AI Drawing Prompt Reference

Draw a prism to demonstrate volume calculation. Start by constructing a base with a circle and two perpendicular segments as the base edges, then rotate these edges to form the lateral faces. Add a vertical segment as the height, using rotations and intersections to define the lateral faces and top face. Finally, connect the base and top to complete the prism, labeling key geometric elements like base edges, height, and lateral faces to clearly illustrate the volume calculation process.
The prompt above was compiled from the original drawing commands and is for reference only.