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Rectangular Prism Volume Investigation

Rectangular Prism Volume Investigation
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2017-06-27 01:40
Solid GeometryGeometric Construction
This example demonstrates how to investigate the volume of a rectangular prism interactively. Core math concepts include volume, subtraction, rational numbers, and combinatorics. Construction highlights the use of GeoGebra commands and objects like Intersect, Circle, OrthogonalLine, Sequence, Polygon, Prism, and Segment. Suitable for middle school and above students to understand volume calculations in solid geometry.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → A
  2. Circle(A, w_1) → c
  3. Circle(A, l_1) → d
  4. Intersect(d, xAxis, 2) → B
  5. Intersect(c, yAxis, 2) → C
  6. OrthogonalLine(C, yAxis) → f
  7. OrthogonalLine(B, xAxis) → g
  8. Intersect(f, g) → D
  9. Sequence(Segment[A + (i * (1, 0, 0)), C + (i * (1, 0, 0))], i, 1, l_1 - 1) → list1
  10. Sequence(Segment[A + (i * (0, 1, 0)), B + (i * (0, 1, 0))], i, 1, w_1 - 1) → list2
  11. Polygon(A, C, D, B) → poly1, a, c_1, d_1, b
  12. Circle(A, length) → k
  13. Circle(A, width) → p
  14. Intersect(k, xAxis, 2) → E
  15. Intersect(p, yAxis, 2) → F
  16. OrthogonalLine(F, yAxis) → i
  17. OrthogonalLine(E, xAxis) → j
  18. Intersect(i, j) → G
  19. Polygon(A, F, G, E) → poly2, a_1, f_1, g_1, e
  20. Prism(poly2, height) → m, H, edgeAH, edgeFI, edgeGJ, edgeEK, edgeHI, edgeIJ, edgeJK, edgeHK, I, J, K, faceAFIH, faceFGJI, faceEGJK, faceAEKH, faceHIJK
  21. Prism(poly1, h_1) → n, L, edgeAL, edgeCM, edgeDN, edgeBO, edgeLM, edgeMN, edgeNO, edgeLO, M, N, O, faceACML, faceCDNM, faceBDNO, faceABOL, faceLMNO
  22. Sequence(Segment[A + (i * (1, 0, 0)), L + (i * (1, 0, 0))], i, 1, l_1 - 1) → list3
  23. Sequence(Segment[C + (i * (1, 0, 0)), M + (i * (1, 0, 0))], i, 1, l_1 - 1) → list4
  24. Sequence(Segment[A + (i * (0, 1, 0)), L + (i * (0, 1, 0))], i, 1, w_1 - 1) → list5
  25. Sequence(Segment[B + (i * (0, 1, 0)), O + (i * (0, 1, 0))], i, 1, w_1 - 1) → list6
  26. Sequence(Segment[L + (i * (1, 0, 0)), M + (i * (1, 0, 0))], i, 1, l_1 - 1) → list7
  27. Sequence(Segment[L + (i * (0, 1, 0)), O + (i * (0, 1, 0))], i, 1, w_1 - 1) → list8
  28. Sequence(Segment[A + (i * (0, 0, 1)), B + (i * (0, 0, 1))], i, 1, h_1 - 1) → list9
  29. Sequence(Segment[A + (i * (0, 0, 1)), C + (i * (0, 0, 1))], i, 1, h_1 - 1) → list10
  30. Sequence(Segment[B + (i * (0, 0, 1)), D + (i * (0, 0, 1))], i, 1, h_1 - 1) → list11
  31. Sequence(Segment[C + (i * (0, 0, 1)), D + (i * (0, 0, 1))], i, 1, h_1 - 1) → list12
  32. Segment(L, H) → l
  33. Segment(H, I) → q
  34. Segment(I, J) → r
  35. Segment(J, G) → s
  36. Segment(G, E) → t
  37. Segment(E, K) → i_1
  38. Segment(L, H) → k_1
  39. Segment(F, I) → n_1
  40. Segment(H, K) → p_1
  41. Segment(K, J) → q_1
  42. Segment(F, G) → r_1
  43. Segment(E, A) → j_1
  44. Segment(F, A) → m_1

AI Drawing Prompt Reference

Draw a rectangular prism, first sketch the bottom and top faces as rectangles, then connect them with vertical edges to form the three-dimensional structure. The bottom and top faces are parallel and equal. Use different colors or line thicknesses to distinguish the faces and edges for a clear view of the volume calculation.
The prompt above was compiled from the original drawing commands and is for reference only.