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Cubic Yards to Cubic Feet Conversion

Cubic Yards to Cubic Feet Conversion
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2015-10-06 08:54
Coordinate GeometrySolid GeometryGeometric Construction
This example demonstrates the conversion from cubic yards to cubic feet. Key mathematical concepts include unit conversion. Using GeoGebra commands such as Point, Cube, and Intersect, a cube model is constructed, and the construction of different faces and edges is shown. Suitable for middle school and above students to learn unit conversion and geometric construction.

GeoGebra Commands & Parameters

  1. Point(Circle[B, Distance[A, B], Segment[A, B]]) → D
  2. Cube(A, B, D) → a, E, faceDEIH, faceFGHI, edgeAE, edgeAB, edgeBD, edgeDE, edgeAF, edgeEI, edgeFI, edgeFG, F, edgeBG, edgeGH, edgeDH, edgeHI, G, H, I, faceABDE, faceAEIF, faceABGF, faceBDHG
  3. Point(Circle[J, Distance[A, J], Segment[A, J]]) → K
  4. Cube(A, J, K) → b, L, faceKLPO, faceMNOP, edgeAL, edgeAJ, edgeJK, edgeKL, edgeAM, edgeLP, edgeMP, edgeMN, M, edgeJN, edgeNO, edgeKO, edgeOP_1, N, O, P, faceAJKL, faceALPM, faceAJNM, faceJKON
  5. Point(Circle[R, Distance[Q, R], Segment[Q, R]]) → S
  6. Cube(Q, R, S) → c, T, faceSTZW, faceUVWZ, edgeQT, edgeQR, edgeRS, edgeST, edgeQU, edgeTZ, edgeUZ, edgeUV, U, edgeRV, edgeVW, edgeSW, edgeWZ, V, W, Z, faceQRST, faceQTZU, faceQRVU, faceRSWV
  7. Point(Circle[A_1, Distance[R, A_1], Segment[R, A_1]]) → B_1
  8. Cube(R, A_1, B_1) → d, C_1, face5, face6, edge2, edge1, edge4, edge6, edge3, edge8, edge10, edge9, D_1, edge5, edge11, edge7, edge12, E_1, F_1, G_1, face1, face3, face2, face4
  9. Point(yAxis) → H_1
  10. Point(Circle[H_1, Distance[I_1, H_1], Segment[I_1, H_1]]) → J_1
  11. Cube(I_1, H_1, J_1) → e, K_1, face11, face12, edge16, edge13, edge14, edge18, edge17, edge20, edge22, edge21, L_1, edge15, edge23, edge19, edge24, M_1, N_1, O_1, face7, face10, face8, face9
  12. Intersect(edgeDE, edgeEI) → P_1
  13. Point(Circle[P_1, Distance[I_1, P_1], Segment[I_1, P_1]]) → Q_1
  14. Point(edge16) → R_1
  15. Point(Circle[R_1, Distance[I_1, R_1], Segment[I_1, R_1]]) → S_1
  16. Cube(I_1, R_1, S_1) → f, T_1, face17, face18, edge26, edge25, edge28, edge30, edge27, edge32, edge34, edge33, U_1, edge29, edge35, edge31, edge36, V_1, W_1, Z_1, face13, face15, face14, face16
  17. Point(Circle[P, Distance[O, P], Segment[O, P]]) → A_2
  18. Point(Circle[(1, 0, 1), Distance[(1, -1, 1), (1, 0, 1)], Segment[(1, -1, 1), (1, 0, 1)]]) → B_2
  19. Intersect(edge24, edge20) → C_2
  20. Point(edge21) → D_2
  21. Point(Circle[D_2, Distance[C_2, D_2], Segment[C_2, D_2]]) → E_2
  22. Cube(C_2, D_2, E_2) → g, F_2, face23, face24, edge38, edge37, edge40, edge42, edge39, edge44, edge46, edge45, G_2, edge41, edge47, edge43, edge48, H_2, I_2, J_2, face19, face21, face20, face22
  23. Point(Circle[(2, 0, 1), Distance[(2, 0, 0), (2, 0, 1)], Segment[(2, 0, 0), (2, 0, 1)]]) → K_2
  24. Cube((2, 0, 0), (2, 0, 1), K_2) → h, L_2, face29, face30, edge50, edge49, edge52, edge54, edge51, edge56, edge58, edge57, M_2, edge53, edge59, edge55, edge60, N_2, O_2, P_2, face25, face27, face26, face28
  25. Point(Circle[(2, 0, 0), Distance[(1, 0, 0), (2, 0, 0)], Segment[(1, 0, 0), (2, 0, 0)]]) → Q_2
  26. Cube((1, 0, 0), (2, 0, 0), Q_2) → i, R_2, face35, face36, edge62, edge61, edge64, edge66, edge63, edge68, edge70, edge69, S_2, edge65, edge71, edge67, edge72, T_2, U_2, V_2, face31, face33, face32, face34
  27. Point(Circle[(1, 1, 1), Distance[(1, 0, 1), (1, 1, 1)], Segment[(1, 0, 1), (1, 1, 1)]]) → W_2
  28. Point(Circle[(1, 3, 1), Distance[(1, 2, 1), (1, 3, 1)], Segment[(1, 2, 1), (1, 3, 1)]]) → Z_2
  29. Cube((1, 2, 1), (1, 3, 1), Z_2) → j, A_3, face41, face42, edge74, edge73, edge76, edge78, edge75, edge80, edge82, edge81, B_3, edge77, edge83, edge79, edge84, C_3, D_3, E_3, face37, face39, face38, face40
  30. Point(Circle[(1, 2, 2), Distance[(1, 1, 2), (1, 2, 2)], Segment[(1, 1, 2), (1, 2, 2)]]) → F_3
  31. Cube((1, 1, 2), (1, 2, 2), F_3) → k, G_3, face47, face48, edge86, edge85, edge88, edge90, edge87, edge92, edge94, edge93, H_3, edge89, edge95, edge91, edge96, I_3, J_3, K_3, face43, face45, face44, face46
  32. Point(Circle[(1, 3, 2), Distance[(1, 2, 2), (1, 3, 2)], Segment[(1, 2, 2), (1, 3, 2)]]) → L_3
  33. Cube((1, 2, 2), (1, 3, 2), L_3) → l, M_3, face53, face54, edge98, edge97, edge100, edge102, edge99, edge104, edge106, edge105, N_3, edge101, edge107, edge103, edge108, O_3, P_3, Q_3, face49, face51, face50, face52
  34. Point(Circle[(2, 0, 1), Distance[(1, 0, 1), (2, 0, 1)], Segment[(1, 0, 1), (2, 0, 1)]]) → R_3
  35. Cube((1, 0, 1), (2, 0, 1), R_3) → m, S_3, face59, face60, edge110, edge109, edge112, edge114, edge111, edge116, edge118, edge117, T_3, edge113, edge119, edge115, edge120, U_3, V_3, W_3, face55, face57, face56, face58
  36. Point(Circle[(3, 0, 1), Distance[(2, 0, 1), (3, 0, 1)], Segment[(2, 0, 1), (3, 0, 1)]]) → Z_3
  37. Cube((2, 0, 1), (3, 0, 1), Z_3) → n, A_4, face65, face66, edge122, edge121, edge124, edge126, edge123, edge128, edge130, edge129, B_4, edge125, edge131, edge127, edge132, C_4, D_4, E_4, face61, face63, face62, face64
  38. Point(Circle[(2, 0, 2), Distance[(1, 0, 2), (2, 0, 2)], Segment[(1, 0, 2), (2, 0, 2)]]) → F_4
  39. Cube((1, 0, 2), (2, 0, 2), F_4) → o, G_4, face71, face72, edge134, edge133, edge136, edge138, edge135, edge140, edge142, edge141, H_4, edge137, edge143, edge139, edge144, I_4, J_4, K_4, face67, face69, face68, face70
  40. Point(Circle[(3, 0, 2), Distance[(2, 0, 2), (3, 0, 2)], Segment[(2, 0, 2), (3, 0, 2)]]) → L_4
  41. Cube((2, 0, 2), (3, 0, 2), L_4) → p, M_4, face77, face78, edge146, edge145, edge148, edge150, edge147, edge152, edge154, edge153, N_4, edge149, edge155, edge151, edge156, O_4, P_4, Q_4, face73, face75, face74, face76
  42. Point(Circle[(3, 1, 0), Distance[(2, 1, 0), (3, 1, 0)], Segment[(2, 1, 0), (3, 1, 0)]]) → R_4
  43. Cube((2, 1, 0), (3, 1, 0), R_4) → q, S_4, face83, face84, edge158, edge157, edge160, edge162, edge159, edge164, edge166, edge165, T_4, edge161, edge167, edge163, edge168, U_4, V_4, W_4, face79, face81, face80, face82
  44. Point(Circle[(3, 1, 1), Distance[(2, 1, 1), (3, 1, 1)], Segment[(2, 1, 1), (3, 1, 1)]]) → Z_4
  45. Cube((2, 1, 1), (3, 1, 1), Z_4) → r, A_5, face89, face90, edge170, edge169, edge172, edge174, edge171, edge176, edge178, edge177, B_5, edge173, edge179, edge175, edge180, C_5, D_5, E_5, face85, face87, face86, face88
  46. Point(Circle[(3, 1, 2), Distance[(2, 1, 2), (3, 1, 2)], Segment[(2, 1, 2), (3, 1, 2)]]) → F_5
  47. Cube((2, 1, 2), (3, 1, 2), F_5) → s, G_5, face95, face96, edge182, edge181, edge184, edge186, edge183, edge188, edge190, edge189, H_5, edge185, edge191, edge187, edge192, I_5, J_5, K_5, face91, face93, face92, face94
  48. Point(Circle[(2, 2, 0), Distance[(1, 2, 0), (2, 2, 0)], Segment[(1, 2, 0), (2, 2, 0)]]) → L_5
  49. Cube((1, 2, 0), (2, 2, 0), L_5) → t, M_5, face101, face102, edge194, edge193, edge196, edge198, edge195, edge200, edge202, edge201, N_5, edge197, edge203, edge199, edge204, O_5, P_5, Q_5, face97, face99, face98, face100
  50. Point(Circle[(3, 2, 0), Distance[(2, 2, 0), (3, 2, 0)], Segment[(2, 2, 0), (3, 2, 0)]]) → R_5
  51. Cube((2, 2, 0), (3, 2, 0), R_5) → u, S_5, face107, face108, edge206, edge205, edge208, edge210, edge207, edge212, edge214, edge213, T_5, edge209, edge215, edge211, edge216, U_5, V_5, W_5, face103, face105, face104, face106
  52. Point(Circle[(2, 0, 1), Distance[(1, 0, 1), (2, 0, 1)], Segment[(1, 0, 1), (2, 0, 1)]]) → Z_5
  53. Point(Circle[(2, 2, 3), Distance[(1, 2, 3), (2, 2, 3)], Segment[(1, 2, 3), (2, 2, 3)]]) → A_6
  54. Point(Circle[(2, 2, 2), Distance[(1, 2, 2), (2, 2, 2)], Segment[(1, 2, 2), (2, 2, 2)]]) → B_6
  55. Cube((1, 2, 2), (2, 2, 2), B_6) → v, C_6, face113, face114, edge218, edge217, edge220, edge222, edge219, edge224, edge226, edge225, D_6, edge221, edge227, edge223, edge228, E_6, F_6, G_6, face109, face111, face110, face112
  56. Point(Circle[(2, 2, 1), Distance[(1, 2, 1), (2, 2, 1)], Segment[(1, 2, 1), (2, 2, 1)]]) → H_6
  57. Cube((1, 2, 1), (2, 2, 1), H_6) → w, I_6, face119, face120, edge230, edge229, edge232, edge234, edge231, edge236, edge238, edge237, J_6, edge233, edge239, edge235, edge240, K_6, L_6, M_6, face115, face117, face116, face118
  58. Point(Circle[(3, 2, 1), Distance[(2, 2, 1), (3, 2, 1)], Segment[(2, 2, 1), (3, 2, 1)]]) → N_6
  59. Cube((2, 2, 1), (3, 2, 1), N_6) → a_1, O_6, face125, face126, edge242, edge241, edge244, edge246, edge243, edge248, edge250, edge249, P_6, edge245, edge251, edge247, edge252, Q_6, R_6, S_6, face121, face123, face122, face124
  60. Point(Circle[(3, 2, 2), Distance[(2, 2, 2), (3, 2, 2)], Segment[(2, 2, 2), (3, 2, 2)]]) → T_6
  61. Cube((2, 2, 2), (3, 2, 2), T_6) → b_1, U_6, face131, face132, edge254, edge253, edge256, edge258, edge255, edge260, edge262, edge261, V_6, edge257, edge263, edge259, edge264, W_6, Z_6, A_7, face127, face129, face128, face130
  62. Cube((1, 1, 2), (2, 1, 2), (2, 2, 2)) → c_1, B_7, face137, face138, edge266, edge265, edge268, edge270, edge267, edge272, edge274, edge273, C_7, edge269, edge275, edge271, edge276, D_7, E_7, F_7, face133, face135, face134, face136
  63. Cube((1, 1, 1), (2, 1, 1), (2, 2, 1)) → d_1, G_7, face143, face144, edge278, edge277, edge280, edge282, edge279, edge284, edge286, edge285, H_7, edge281, edge287, edge283, edge288, I_7, J_7, K_7, face139, face141, face140, face142
  64. Cube((1, 1, 0), (2, 1, 0), (2, 2, 0)) → e_1, L_7, face149, face150, edge290, edge289, edge292, edge294, edge291, edge296, edge298, edge297, M_7, edge293, edge299, edge295, edge300, N_7, O_7, P_7, face145, face147, face146, face148
  65. Point(edgeEI) → Q_7
  66. Point(edgeDE) → R_7
  67. Point(edgeFI) → S_7
  68. Point(edgeDE) → T_7
  69. Point(edge79) → U_7
  70. Point(edge198) → V_7
  71. Point(edge96) → W_7