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Rectangular Prism Volume Practice

Rectangular Prism Volume Practice
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2016-12-15 01:17
Coordinate GeometrySolid Geometry
This example demonstrates the calculation of the volume of a rectangular prism. Key mathematical concepts include the volume calculation in solid geometry. Using GeoGebra commands such as Intersect, Random, Circle, etc., a rectangular prism can be constructed and its volume calculated. Suitable for middle school and above students for geometric construction and volume calculation practice.

GeoGebra Commands & Parameters

  1. Intersect(zAxis, xAxis) → A
  2. Random(1, 11) → A2
  3. Random(1, 11) → B2
  4. Random(1, 11) → C2
  5. Random(1, 4) → a
  6. Circle(A, A2, zAxis) → c
  7. Circle(A, B2, zAxis) → d
  8. Circle(A, C2, yAxis) → e
  9. Intersect(yAxis, c) → B, C_1
  10. Intersect(xAxis, d) → D, E_1
  11. Intersect(zAxis, e) → E, G_1
  12. Plane(A, E, B) → b
  13. OrthogonalLine(B, b) → f
  14. OrthogonalLine(A, b) → g
  15. Plane(A, D, E) → h_2
  16. OrthogonalLine(D, h_2) → i
  17. Intersect(i, f) → C
  18. Polygon(A, B, C, D) → poly1, a_1, b_1, h_1, d_1
  19. Prism(poly1, (-C2)) → j, I_1, edgeAI, edgeBJ, edgeHK, edgeDL, edgeIJ, edgeJK, edgeKL, edgeIL, F, G, J, faceABJI, faceBHKJ, faceDHKL, faceADLI, faceIJKL
  20. Circle(A, h, yAxis) → k
  21. Circle(A, l, xAxis) → p
  22. Circle(A, w, zAxis) → q
  23. Intersect(xAxis, q) → M, N
  24. Intersect(yAxis, p) → O, P
  25. Intersect(zAxis, k) → Q, R
  26. Segment(A, O) → l_1
  27. Segment(Q, A) → m
  28. Segment(A, M) → n
  29. Line(M, l_1) → r
  30. Line(O, n) → s
  31. Intersect(s, r) → S
  32. Polygon(A, O, S, M) → poly2, a_2, o, s_1, m_1
  33. Sequence(Segment[A + (i * (1, 0, 0)), O + (i * (1, 0, 0))], i, 1, w - 1) → list1
  34. Sequence(Segment[A + (i * (0, 1, 0)), M + (i * (0, 1, 0))], i, 1, l - 1) → list2
  35. Sequence(Segment[A + (i * (0, 0, 1)), M + (i * (0, 0, 1))], i, 1, h - 1) → list3
  36. Sequence(Segment[A + (i * (0, 0, 1)), O + (i * (0, 0, 1))], i, 1, h - 1) → list4
  37. Sequence(Segment[M + (i * (0, 0, 1)), S + (i * (0, 0, 1))], i, 1, h - 1) → list5
  38. Sequence(Segment[O + (i * (0, 0, 1)), S + (i * (0, 0, 1))], i, 1, h - 1) → list6
  39. Line(Q, a_2) → t
  40. Line(Q, m_1) → f_1
  41. Line(M, m) → g_1
  42. Line(O, m) → i_1
  43. Intersect(t, i_1) → T
  44. Intersect(g_1, f_1) → U
  45. Line(U, t) → j_1
  46. Line(T, f_1) → k_1
  47. Intersect(j_1, k_1) → V
  48. Polygon(Q, T, V, U) → poly3, q_1, t_1, v, u
  49. Sequence(Segment[Q + (i * (1, 0, 0)), T + (i * (1, 0, 0))], i, 1, w - 1) → list7
  50. Sequence(Segment[Q + (i * (0, 1, 0)), U + (i * (0, 1, 0))], i, 1, l - 1) → list8
  51. Sequence(Segment[A + (i * (0, 0, 1)), O + (i * (0, 0, 1))], i, 1, h - 1) → list9
  52. Sequence(Segment[A + (i * (0, 1, 0)), Q + (i * (0, 1, 0))], i, 1, l - 1) → list10
  53. Sequence(Segment[M + (i * (0, 1, 0)), U + (i * (0, 1, 0))], i, 1, l - 1) → list13
  54. Sequence(Segment[A + (i * (1, 0, 0)), Q + (i * (1, 0, 0))], i, 1, w - 1) → list11
  55. Sequence(Segment[O + (i * (1, 0, 0)), T + (i * (1, 0, 0))], i, 1, w - 1) → list12
  56. Polygon(T, O, A, Q) → poly4, t_2, o_1, a_3, q_2
  57. Polygon(T, V, S, O) → poly5, t_3, v_1, s_2, o_2
  58. Polygon(Q, U, M, A) → poly6, q_3, u_1, m_2, a_4
  59. Polygon(U, V, S, M) → poly7, u_2, v_2, s_3, m_3
  60. Textfield(w_1) → InputBox1

AI Drawing Prompt Reference

Draw a rectangular prism with randomly generated base circle radii and positions, determine the vertices of the prism through the intersections of axes and circles, then draw the faces of the prism and fill the interior with lines to demonstrate the volume calculation process.
The prompt above was compiled from the original drawing commands and is for reference only.