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Dynamic Box Volume: Adjust Length, Width, and Height

Dynamic Box Volume: Adjust Length, Width, and Height
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2012-11-30 21:07
PolygonSolid GeometryTransformationGeometric Construction
This GeoGebra example demonstrates an interactive rectangular prism model in which users can change the length, width, and height to observe the box volume changing in real time. The core mathematical concept is the solid geometry volume formula V = length × width × height, highlighting the proportional relationship between linear dimensions and volume in three-dimensional space. Construction points: the example uses GeoGebra commands such as Line, OrthogonalLine, Circle, Polygon, Distance, Rotate, Dilate, Midpoint, If, Segment, and Locus, together with objects including points AA, BB, CC, segments a, b, c, l, and labels such as br, d, e, D, E, F, G to build the box geometry and dynamic controls. It is suitable for middle school geometry (grades 7–9), upper elementary volume introductions, and classroom demonstrations that help students develop an intuitive understanding of how box dimensions determine volume.

GeoGebra Commands & Parameters

  1. Line(AA, BB) → a
  2. OrthogonalLine(CC, a) → b
  3. OrthogonalLine(CC, b) → c
  4. Circle(CC, l) → d
  5. Circle(CC, br) → e
  6. Intersect(d, c) → D, E
  7. Intersect(e, b) → F, G
  8. OrthogonalLine(G, b) → f
  9. OrthogonalLine(D, c) → g
  10. OrthogonalLine(F, b) → h
  11. OrthogonalLine(E, c) → i
  12. Intersect(f, i) → H
  13. Intersect(g, f) → I
  14. Intersect(g, h) → J
  15. Intersect(h, i) → K
  16. Polygon(H, I, J, K) → mangekant1, h_1, i_1, j, k
  17. OrthogonalLine(Rotate, h_1) → m
  18. OrthogonalLine(Rotate, k) → n
  19. Intersect(h_1, m) → M
  20. Intersect(k, n) → N
  21. Distance(Rotate, M) → avstandLM
  22. Distance(Rotate, N) → avstandLN
  23. OrthogonalLine(O, a) → p
  24. OrthogonalLine(O, p) → q
  25. Circle(O, size) → r
  26. Intersect(r, q) → P, Q
  27. Intersect(r, p) → R, S
  28. OrthogonalLine(S, p) → s
  29. OrthogonalLine(P, q) → t
  30. OrthogonalLine(R, p) → a_1
  31. OrthogonalLine(Q, q) → b_1
  32. Intersect(s, b_1) → T
  33. Intersect(s, t) → U
  34. Intersect(a_1, t) → V
  35. Intersect(a_1, b_1) → W
  36. Polygon(U, T, W, V) → mangekant2, u, t_1, w, v
  37. Rotate(U, ho, O) → U'
  38. Rotate(T, ho, O) → T'
  39. Rotate(W, ho, O) → W'
  40. Rotate(V, ho, O) → V'
  41. Polygon(U', T', W', V') → mangekant2', u', t', w', v'
  42. OrthogonalLine(T', q) → c_1
  43. OrthogonalLine(W', q) → d_1
  44. OrthogonalLine(V', q) → e_1
  45. OrthogonalLine(U', q) → f_1
  46. OrthogonalLine(T', q) → g_1
  47. OrthogonalLine(V', q) → j_1
  48. OrthogonalLine(U', q) → k_1
  49. OrthogonalLine(W', q) → l_1
  50. Intersect(g_1, q) → Z
  51. Intersect(l_1, q) → A_1
  52. Intersect(q, k_1) → B_1
  53. Intersect(q, j_1) → C_1
  54. Distance(Z, T') → avstandZT'
  55. Distance(B_1, U') → avstandB1U'
  56. Dilate(T', l1, Z) → T''
  57. Dilate(W', l1, A_1) → W''
  58. Dilate(U', l1, B_1) → U''
  59. Dilate(V', l1, C_1) → V''
  60. Polygon(T'', W'', V'', U'') → mangekant3, t'', w'', v'', u''
  61. Midpoint(W'', V'') → D_1
  62. Midpoint(V'', U'') → E_1
  63. Distance(O, D_1) → avstandOD1
  64. Distance(O, E_1) → avstandOE1
  65. If(((-π < ve) ∧ (ve < (-π) / 2) ∨ (π / 2 < ve) ∧ (ve < π)) ∧ ((-π) / 2 < ho) ∧ (ho < π / 2) ∨ ((-π) / 2 < ve) ∧ (ve < π / 2) ∧ ((-π < ho) ∧ (ho < (-π) / 2) ∨ (π / 2 < ho) ∧ (ho < π)), van / (size - xp) + 3, (-van) / (size - xp) - 3) → ix
  66. Dilate(D_1, ix, O) → F_1
  67. If((0 < ho) ∧ (ho < π) ∧ ((-π) / 2 < ve) ∧ (ve < π / 2) ∨ (-π < ho) ∧ (ho < 0) ∧ ((-π < ve) ∧ (ve < (-π) / 2) ∨ (π / 2 < ve) ∧ (ve < π)), van / (size - yp) + 3, (-van) / (size - yp) - 3) → iy
  68. Dilate(E_1, iy, O) → G_1
  69. If((-π < ve) ∧ (ve < (-π) / 2) ∨ (0 < ve) ∧ (ve < π / 2), (-van) / (size - zp) - 3, van / (size - zp) + 3) → iz
  70. Circle(O, size) → p_1
  71. Circle(O, zp) → q_1
  72. Intersect(q_1, p) → J_1, K_1
  73. Dilate(K_1, iz, O) → H_1
  74. Dilate(D_1, xpos, O) → I_1
  75. Dilate(D_1, xneg, O) → L_1
  76. Dilate(E_1, ypos, O) → M_1
  77. Dilate(E_1, yneg, O) → N_1
  78. Line(M_1, F_1) → m_1
  79. Line(N_1, F_1) → n_1
  80. Line(L_1, G_1) → r_1
  81. Line(I_1, G_1) → s_1
  82. Intersect(n_1, r_1) → O_1
  83. Intersect(m_1, r_1) → P_1
  84. Intersect(s_1, m_1) → Q_1
  85. Intersect(s_1, n_1) → R_1
  86. Polygon(P_1, O_1, R_1, Q_1) → mangekant4, p_2, o_1, r_2, q_2
  87. Dilate(K_1, zpos, O) → S_1
  88. Dilate(K_1, zneg, O) → T_1
  89. Segment(I_1, L_1) → a_2
  90. Segment(N_1, M_1) → b_2
  91. Line(F_1, S_1) → c_2
  92. Line(T_1, F_1) → d_2
  93. Line(S_1, G_1) → e_2
  94. Line(T_1, G_1) → f_2
  95. Line(H_1, N_1) → g_2
  96. Line(H_1, I_1) → h_2
  97. Line(H_1, L_1) → i_2
  98. Line(H_1, M_1) → j_2
  99. Intersect(g_2, e_2) → V_1
  100. Intersect(g_2, f_2) → W_1
  101. Intersect(e_2, j_2) → Z_1
  102. Intersect(f_2, j_2) → A_2
  103. Line(V_1, F_1) → k_2
  104. Line(Z_1, F_1) → l_2
  105. Line(W_1, F_1) → m_2
  106. Line(A_2, F_1) → n_2
  107. Intersect(i_2, c_2) → B_2
  108. Intersect(i_2, d_2) → C_2
  109. Intersect(c_2, h_2) → D_2
  110. Intersect(h_2, d_2) → E_2
  111. Line(B_2, G_1) → s_2
  112. Line(D_2, G_1) → t_2
  113. Line(E_2, G_1) → a_3
  114. Line(C_2, G_1) → b_3
  115. Intersect(k_2, s_2) → F_2
  116. Intersect(s_2, l_2) → G_2
  117. Intersect(t_2, l_2) → H_2
  118. Intersect(t_2, k_2) → I_2
  119. Intersect(m_2, b_3) → J_2
  120. Intersect(m_2, a_3) → K_2
  121. Intersect(a_3, n_2) → L_2
  122. Intersect(n_2, b_3) → M_2
  123. Segment(F_2, G_2) → c_3
  124. Segment(G_2, H_2) → d_3
  125. Segment(H_2, I_2) → e_3
  126. Segment(I_2, F_2) → f_3
  127. Segment(F_2, J_2) → g_3
  128. Segment(I_2, K_2) → h_3
  129. Segment(L_2, H_2) → i_3
  130. Segment(G_2, M_2) → j_3
  131. Segment(M_2, L_2) → k_3
  132. Segment(L_2, K_2) → l_3
  133. Segment(K_2, J_2) → m_3
  134. Segment(J_2, M_2) → n_3
  135. Segment(T_1, S_1) → p_3
  136. Dilate(I_1, enxm, O) → S_2
  137. Line(S_2, G_1) → g_4
  138. Intersect(q_2, g_4) → S_3
  139. Intersect(o_1, g_4) → P_4
  140. Dilate(M_1, enym, O) → N_5
  141. Line(N_5, F_1) → h_6
  142. Intersect(p_2, h_6) → H_6
  143. Intersect(r_2, h_6) → E_7
  144. Dilate(I_1, x1, O) → A
  145. Dilate(I_1, x1m, O) → B
  146. Dilate(M_1, y1, O) → C
  147. Dilate(M_1, y1m, O) → L
  148. Line(L, F_1) → q_3
  149. Line(C, F_1) → r_3
  150. Line(B, G_1) → s_3
  151. Line(A, G_1) → t_3
  152. Intersect(r_3, s_3) → N_2
  153. Intersect(q_3, s_3) → O_2
  154. Intersect(r_3, t_3) → P_2
  155. Intersect(q_3, t_3) → Q_2
  156. Polygon(O_2, Q_2, P_2, N_2) → poly1, o_2, q_4, p_4, n_4
  157. Dilate(I_1, x3, O) → R_2
  158. Dilate(I_1, x2, O) → T_2
  159. Dilate(I_1, x3m, O) → U_2
  160. Dilate(I_1, x2m, O) → V_2
  161. Dilate(M_1, y3, O) → W_2
  162. Dilate(M_1, y2, O) → Z_2
  163. Dilate(M_1, y3m, O) → A_3
  164. Dilate(M_1, y2m, O) → B_3
  165. Dilate(S_1, z1, O) → C_3
  166. Line(V_2, G_1) → a_4
  167. Line(R_2, G_1) → b_4
  168. Line(Z_2, F_1) → c_4
  169. Line(B_3, F_1) → d_4
  170. Intersect(a_4, d_4) → D_3
  171. Intersect(c_4, a_4) → E_3
  172. Intersect(c_4, b_4) → F_3
  173. Intersect(d_4, b_4) → G_3
  174. Polygon(D_3, G_3, F_3, E_3) → poly2, d_5, g_5, f_4, e_4
  175. Line(H_1, T_2) → h_4
  176. Line(H_1, U_2) → i_4
  177. Line(H_1, A_3) → j_4
  178. Line(H_1, W_2) → k_4
  179. Line(C_3, G_1) → l_4
  180. Line(T_2, G_1) → m_4
  181. Line(U_2, G_1) → r_4
  182. Line(A_3, F_1) → s_4
  183. Line(W_2, F_1) → t_4
  184. Line(C_3, F_1) → a_5
  185. Intersect(i_4, a_5) → H_3
  186. Intersect(h_4, a_5) → I_3
  187. Intersect(j_4, l_4) → J_3
  188. Intersect(k_4, l_4) → K_3
  189. Intersect(c_4, m_4) → L_3
  190. Intersect(m_4, d_4) → M_3
  191. Intersect(r_4, c_4) → N_3
  192. Intersect(r_4, d_4) → O_3
  193. Intersect(s_4, a_4) → P_3
  194. Intersect(b_4, s_4) → Q_3
  195. Intersect(t_4, b_4) → R_3
  196. Intersect(t_4, a_4) → T_3
  197. Line(H_1, Q_3) → b_5
  198. Line(H_1, P_3) → c_5
  199. Line(H_1, R_3) → e_5
  200. Line(H_1, T_3) → f_5
  201. Line(H_1, M_3) → h_5
  202. Line(H_1, L_3) → i_5
  203. Line(H_1, O_3) → j_5
  204. Line(H_1, N_3) → k_5
  205. Line(I_3, G_1) → l_5
  206. Line(H_3, G_1) → m_5
  207. Line(J_3, F_1) → n_5
  208. Line(K_3, F_1) → p_5
  209. Intersect(j_5, m_5) → U_3
  210. Intersect(k_5, m_5) → V_3
  211. Polygon(D_3, U_3, V_3, E_3) → poly3, d_6, u_3, v_3, e_6
  212. Intersect(f_5, p_5) → W_3
  213. Intersect(e_5, p_5) → Z_3
  214. Polygon(E_3, W_3, Z_3, F_3) → poly4, e_7, w_3, z_3, f_6
  215. Intersect(c_5, n_5) → A_4
  216. Intersect(b_5, n_5) → B_4
  217. Polygon(A_4, D_3, G_3, B_4) → poly5, a_6, d_7, g_6, b_6
  218. Intersect(i_5, l_5) → C_4
  219. Intersect(h_5, l_5) → D_4
  220. Polygon(G_3, D_4, C_4, F_3) → poly6, g_7, d_8, c_6, f_7
  221. Intersect(a_4, q_3) → E_4
  222. Intersect(b_4, q_3) → F_4
  223. Intersect(t_3, d_4) → G_4
  224. Intersect(t_3, c_4) → H_4
  225. Intersect(r_3, b_4) → I_4
  226. Intersect(r_3, a_4) → J_4
  227. Intersect(d_4, s_3) → K_4
  228. Intersect(s_3, c_4) → L_4
  229. Polygon(L_4, E_3, J_4, N_2) → poly7, l_6, e_8, j_6, n_6
  230. Polygon(E_4, D_3, K_4, O_2) → poly8, e_9, d_9, k_6, o_3
  231. Polygon(I_4, F_3, H_4, P_2) → poly9, i_6, f_8, h_7, p_6
  232. Polygon(Q_2, G_4, G_3, F_4) → poly10, q_5, g_8, g_9, f_9
  233. Segment(O_2, N_2) → r_5
  234. Segment(O_2, Q_2) → s_5
  235. Segment(Q_2, P_2) → t_5
  236. Segment(P_2, N_2) → m_6
  237. Segment(L_4, N_2) → q_6
  238. Segment(N_2, J_4) → r_6
  239. Segment(K_4, O_2) → s_6
  240. Segment(O_2, E_4) → t_6
  241. Segment(F_4, Q_2) → a_7
  242. Segment(Q_2, G_4) → b_7
  243. Segment(H_4, P_2) → c_7
  244. Segment(P_2, I_4) → i_7
  245. Segment(O, C_3) → j_7
  246. Segment(D_3, E_3) → k_7
  247. Segment(E_3, F_3) → l_7
  248. Segment(F_3, G_3) → m_7
  249. Segment(G_3, D_3) → n_7
  250. Segment(D_3, K_4) → p_7
  251. Segment(D_3, E_4) → q_7
  252. Segment(G_3, F_4) → r_7
  253. Segment(G_3, G_4) → s_7
  254. Segment(F_3, H_4) → t_7
  255. Segment(F_3, I_4) → a_8
  256. Segment(E_3, J_4) → b_8
  257. Segment(E_3, L_4) → c_8
  258. Dilate(I_1, hei, O) → M_4
  259. Dilate(S_1, vol, O) → N_4
  260. Line(N_4, F_1) → h_8
  261. Line(H_1, M_4) → i_8
  262. Intersect(h_8, i_8) → O_4
  263. Locus(O_4, height) → loc1
  264. Segment(O, S_1) → j_8
  265. Segment(O, I_1) → k_8
  266. Segment(O_4, N_4) → l_8
  267. Segment(O_4, M_4) → m_8
  268. Segment(O, M_4) → n_8
  269. Segment(T_3, N_2) → p_8
  270. Segment(D_3, U_3) → q_8
  271. Segment(U_3, V_3) → r_8
  272. Segment(V_3, E_3) → s_8
  273. Segment(E_3, W_3) → t_8
  274. Segment(W_3, Z_3) → a_9
  275. Segment(Z_3, F_3) → b_9
  276. Segment(C_4, F_3) → c_9
  277. Segment(C_4, D_4) → h_9
  278. Segment(D_4, G_3) → i_9
  279. Segment(G_3, B_4) → j_9
  280. Segment(B_4, A_4) → k_9
  281. Segment(A_4, D_3) → l_9
  282. Polygon(D_3, E_3, F_3, G_3) → poly11, d_{10}, e_{10}, f_{10}, g_{10}

AI Drawing Prompt Reference

Draw a rectangular prism that can be adjusted in length, width, and height by moving points A, B, and C. Start by drawing the base AB, then draw a line segment CC perpendicular to AB, followed by line segments AA and BB perpendicular to CC. Use rotation and translation to generate the other edges of the prism, and finally connect the points to form the rectangular prism.
The prompt above was compiled from the original drawing commands and is for reference only.