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Optimizing the Volume of an Open Box

Optimizing the Volume of an Open Box
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2018-06-11 00:04
FunctionOptimizationGeometric Construction
This example demonstrates how to optimize the volume of an open box by adjusting its dimensions. Key mathematical concepts include geometric construction, function graphing, and optimization. Using GeoGebra commands such as Polygon, Line, and Rotate, the process of changing the box's volume is dynamically illustrated. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  1. Polygon((a, a, 0), (L - a, a, 0), (L - a, W - a, 0), (a, W - a, 0)) → polyBase, f, g, h, i
  2. Polygon((a, 0, 0), (L - a, 0, 0), (L - a, a, 0), (a, a, 0)) → poly1, j, k, l, m
  3. Line((a, a, 0), (L - a, a, 0)) → ax1
  4. Rotate(poly1, (-b), ax1) → poly1'
  5. Polygon((0, a, 0), (0, W - a, 0), (a, W - a, 0), (a, a, 0)) → poly2, n, p, q, r
  6. Line((a, a, 0), (a, W - a, 0)) → ax2
  7. Rotate(poly2, b, ax2) → poly2'
  8. Polygon((a, W - a, 0), (L - a, W - a, 0), (L - a, W, 0), (a, W, 0)) → poly3, s, t, c, d
  9. Line((a, W - a, 0), (L - a, W - a, 0)) → ax3
  10. Rotate(poly3, b, ax3) → poly3'
  11. Polygon((L - a, a, 0), (L - a, W - a, 0), (L, W - a, 0), (L, a, 0)) → poly4, e, f_1, g_1, h_1
  12. Line((L - a, a, 0), (L - a, W - a, 0)) → ax4
  13. Rotate(poly4, (-b), ax4) → poly4'
  14. Polygon((0, 0, 0), (L, 0, 0), (L, W, 0), (0, W, 0)) → poly0, i_1, j_1, k_1, l_1