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Variable Cube: Interactive Exploration of Edge Length and Volume

Variable Cube: Interactive Exploration of Edge Length and Volume
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2018-04-27 03:11
PolygonSolid GeometryGeometric ConstructionSlider Animation
This GeoGebra example constructs an interactive cube whose edge length can be dynamically adjusted, demonstrating how changes in the side length affect volume, surface area, and diagonal planes. Core mathematical concepts include solid geometry formulas for prism volume and surface area, spatial coordinate geometry, and parametric modeling using sliders. Construction highlights: the Polygon command creates the base square, Prism generates the 3D solid, and Angle marks dihedral angles; variables n, A, C, D, B define vertex coordinates, while buttons (button1-3) and text boxes (text1-4) display real-time measurements. Suitable for middle school geometry or introductory college solid geometry, this example aids in understanding parametric 3D modeling and dynamic visualization.

GeoGebra Commands & Parameters

  1. Polygon(A, B, C, D) → q1, a, b, c, d
  2. Prism(q1, n) → f, I, edgeAI, edgeBJ, edgeCK, edgeDL, edgeIJ, edgeJK, edgeKL, edgeIL, J, K, L, faceABJI, faceBCKJ, faceCDLK, faceADLI, faceIJKL
  3. Polygon(E, F, G, H, M, N, O, P) → poly1, e_1, f_1, g, h, m, n_1, o, p
  4. Prism(poly1, 0) → i, Q, faceFGSR, faceGHTS, faceHMUT, faceMNVU, faceNOWV, faceOPZW, faceEPZQ, faceQRSTUVWZ, edgeEQ, edgeFR, R, edgeGS, edgeHT, edgeMU, edgeNV, edgeOW, edgePZ, edgeQR, edgeRS, edgeST, edgeTU, S_2, edgeUV, edgeVW, edgeWZ, edgeQZ, T, U, V, W, Z, faceEFRQ
  5. Prism(faceQRSTUVWZ, k) → l, I_1, face12, face13, face14, face15, face16, face17, face11, face18, edge17, edge18, J_1, edge19, edge20, edge21, edge22, edge23, edge24, edge25, edge27, edge28, edge29, K_1, edge30, edge31, edge32, edge26, L_1, M_1, N_1, O_1, P_1, face10
  6. Polygon(A_1, B_1, 4) → poly2, q, r, s, t, C_1, D_1
  7. Polygon(E_1, F_1, 8) → poly3, g_1, H_1, Q_1, R_1, S_1, T_1, h_1, i_1, j_1, k_1, l_1, m_1, p_1, G_1
  8. Polygon(U_1, V_1, W_1, Z_1, A_2) → poly4, u_1, v_1, w_1, z_1, a_2
  9. Polygon(S, B_2, C_2, D_2, E_2) → poly5, s_1, b_2, c_2, d_2, e_2
  10. Angle(E_2, D_2, C_2) → α
  11. Angle(C_2, B_2, S) → β
  12. Angle(D_2, C_2, B_2) → γ
  13. Angle(A_2, Z_1, W_1) → δ
  14. Angle(W_1, V_1, U_1) → ε
  15. Angle(Z_1, W_1, V_1) → ζ
  16. Polygon(F_2, G_2, H_2) → t1, h_2, f_2, g_2
  17. Polygon(I_2, J_2, K_2) → t2, k_2, i_2, j_2
  18. Polygon(L_2, M_2, 6) → poly6, q_1, Q_2, r_1, t_1, b_1, c_1, d_1, N_2, O_2, P_2
  19. Polygon(L_3, M_3, 6) → poly6_1, q_2, Q_3, r_2, t_2, b_3, c_3, d_3, N_3, O_3, P_3
  20. Polygon(R_2, T_2, 3) → poly7, l_2, m_2, n_2, U_2
  21. Polygon(V_2, W_2, 3) → poly8, p_2, s_2, f_3, Z_2
  22. Polygon(A_3, B_3, 5) → poly9, g_3, h_3, i_3, j_3, k_3, C_3, D_3, E_3
  23. Polygon(F_3, G_3, 5) → poly10, l_3, m_3, n_3, p_3, q_3, H_3, I_3, J_3
  24. Polygon(K_3, R_3, 4) → poly11, r_3, s_3, t_3, a_3, S_3, T_3
  25. Polygon(U_3, V_3, 4) → poly12, e_3, f_4, g_4, h_4, W_3, Z_3