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Composite Solid Investigation

Composite Solid Investigation
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2017-08-08 23:42
VectorTrigonometrySolid GeometryGeometric Construction
This example demonstrates the construction of a composite solid formed by a cylinder and a prism, exploring key volume and surface area questions. It involves core concepts like solid geometry, volume calculation, surface area calculation, integers, median value, cosine, and 2D vectors. The construction utilizes commands such as Segment, Ray, Point, Line, OrthogonalLine, Intersect, Vector, Translate, Midpoint, Sphere, CircleArc, Surface, CircleSector, and Polygon. Suitable for high school students to understand composite solids and for math competition preparation.

GeoGebra Commands & Parameters

  1. Segment(B, A) → f
  2. Ray(A, C) → g
  3. Point(g) → E
  4. Line(E, D) → h
  5. OrthogonalLine(B, h, space) → i
  6. Intersect(i, h) → F
  7. Segment(B, F) → j
  8. Segment(F, E) → k
  9. Ray(A, G) → l
  10. Point(l) → H
  11. Vector(A, H) → u
  12. Translate(E, u) → E'
  13. Translate(F, u) → F'
  14. Translate(B, u) → B'
  15. Midpoint(B', H) → I
  16. Midpoint(F', E') → J
  17. Ray((0, 0, 0), (0, 0, 1)) → m
  18. Sphere(I, H) → a
  19. Intersect(m, a) → K, L
  20. Ray(D, J) → n
  21. Sphere(J, E') → b
  22. Intersect(n, b) → M, N
  23. Segment(B', B) → p
  24. Segment(B', F') → q
  25. Segment(F', F) → s
  26. Segment(E, E') → t
  27. Segment(E', F') → c
  28. Segment(A, H) → d
  29. Segment(H, E') → e
  30. Segment(H, B') → f_1
  31. CircleArc(I, H, L) → c_1
  32. Intersect(m, c_1, 1) → O
  33. CircleArc(I, O, B') → d_1
  34. CircleArc(J, E', N) → e_1
  35. Point(e_1) → P
  36. CircleArc(J, P, F') → g_1
  37. Surface(x(I) + (r * cos(u)), y(I) + v, z(I) + (r * sin(u)), u, 0, π, v, y(I), y(J)) → o
  38. CircleSector(I, H, O) → h_1
  39. CircleSector(I, O, B') → k_1
  40. Polygon(B, A, H, B') → poly1, b_1, a_1, h_2, b'
  41. Polygon(A, E, E', H) → poly2, a_2, e_2, e', h_3
  42. CircleSector(J, N, E') → q_1
  43. CircleSector(J, F', N) → p_1
  44. Polygon(E, F, F', E') → poly3, e_3, f_2, f', e'_1
  45. Polygon(B, B', F', F) → poly4, b_2, b'_1, f'_1, f_3
  46. Segment(A, E) → i_1
  47. Segment(A, E) → j_1

AI Drawing Prompt Reference

Draw a composite solid formed by a cylinder and a prism, demonstrating volume and surface area calculations. Start by sketching the bases of the cylinder and prism, then connect corresponding vertices to form the sides. Next, calculate and plot midpoints, vectors, tangents, and arcs, then fill the sides with surfaces and sectors, and use polygons for the bases to fully represent the 3D shape of the composite solid.
The prompt above was compiled from the original drawing commands and is for reference only.