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Differentiation - Cuboid Optimisation

Differentiation - Cuboid Optimisation
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2015-05-18 20:30
Solid GeometryCalculusOptimization
This example demonstrates how to find the dimensions of a cuboid that minimize surface area under a fixed volume using calculus. Key concepts include derivatives, optimization, and solid geometry. Construction involves GeoGebra commands like Polygon, a, A, B, C, D, etc. Suitable for high school students or college freshmen learning calculus and geometry.

GeoGebra Commands & Parameters

  1. Polygon(D, C, B, A) → poly1, d, c, b_1, a_1
  2. Polygon(E, F, D, A) → poly2, e, f, d_1, a_2
  3. Polygon(D, H, G, C) → poly3, d_2, h, g, c_1
  4. Polygon(J, A, B, I) → poly4, j, a_3, b_2, i
  5. Polygon(B, K, L, C) → poly5, b_3, k, l, c_2
  6. Polygon(N, P, O, M) → poly6, n, p, o, m
  7. Polygon(R, N, M, Q) → poly7, r, n_1, m_1, q
  8. Polygon(Q, M, O, S) → poly8, q_1, m_2, o_1, s
  9. Polygon(R, T, P, N) → poly9, r_1, t, p_1, n_2
  10. Polygon(R, T, S, Q) → poly10, r_2, t_1, s_1, q_2
  11. Polygon(T, P, O, S) → poly11, t_2, p_2, o_2, s_2
  12. Polygon(U, V, Z, W) → poly12, u_1, v_1, z_1, w
  13. Polygon(A_1, C_1, D_1, B_1) → poly13, a_4, c_3, d_3, b_4

AI Drawing Prompt Reference

Draw a cuboid and optimize its dimensions to minimize the surface area while keeping the volume constant. Start by drawing four vertices A, B, C, and D, then connect them to form the base ABCD, side ADEA, side BCFB, and side CDHC. Continue by adding other vertices and faces such as E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, and Z, and connect them to form the remaining faces.
The prompt above was compiled from the original drawing commands and is for reference only.