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Right Square Prism Juice Container Design

Right Square Prism Juice Container Design
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2015-04-27 12:35
Solid GeometryCalculusOptimizationParametric EquationGeometric Construction
This example demonstrates the construction of a box with square bases and top, having a capacity of 2 liters, using GeoGebra. It involves core mathematical concepts like solid geometry, volume calculation, integral applications, parametric equations, and optimization design. Key GeoGebra commands and objects used in the construction include OrthogonalLine, Point, Circle, Intersect, Polygon, Prism, Segment, and Min. Suitable for high school and above students learning solid geometry, calculus optimization, and parametric equations, as well as industrial design education.

GeoGebra Commands & Parameters

  1. OrthogonalLine(A, xAxis) → a
  2. Point(yAxis) → B
  3. Circle(B, A) → c
  4. Intersect(c, yAxis) → C, D
  5. OrthogonalLine(D, yAxis) → b
  6. OrthogonalLine(C, yAxis) → d
  7. Intersect(c, xAxis, 1) → E
  8. OrthogonalLine(E, xAxis) → f
  9. Intersect(d, f) → F
  10. Intersect(b, f) → G
  11. Intersect(a, d) → H
  12. Intersect(a, b) → I
  13. Polygon(G, I, H, F) → poly1, g, i, h_1, f_1
  14. Prism(poly1, h) → k, N, edgeGN, edgeIO, edgeHP, edgeFQ, edgeNO, edgeOP, edgePQ, edgeNQ, O, P, Q, faceGION, faceHIOP, faceFHPQ, faceFGNQ, faceNOPQ
  15. Segment(J, L) → j
  16. Segment(L, K) → m
  17. Segment(A, B) → p
  18. Min(Area2, 0.1, 2.5) → M