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Optimal Cake GeoGebra Model

Optimal Cake GeoGebra Model
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2016-08-27 00:32
TrigonometrySolid GeometryMatrixOptimizationGeometric Construction
This GeoGebra example models the 'Optimal Cake' optimization problem, demonstrating how to maximize the volume of a cylindrical cake using geometric construction, trigonometric functions, symmetry, and matrix transformations. The construction employs GeoGebra commands such as Point, Circle, Cone, and Cylinder, working with labeled objects to explore volume constraints and optimal configurations. It serves as a visual aid for calculus, geometry, and mathematical modeling students and educators, illustrating practical applications of rational numbers, trigonometric optimization, and spatial reasoning.

GeoGebra Commands & Parameters

  1. Point(Ray[(0, 0, 0), (0, 0, 1)]) → A
  2. Point(Ray[(0, 0, 0), (1, 0, 0)]) → B
  3. Circle(B, (0, x(B), 0), ((-x(B)), 0, 0)) → e
  4. Cone(e, z(A)) → a, a_2, a_3
  5. Point(Segment[B, A]) → D
  6. Point(Segment[D, A]) → E
  7. Point(Segment[E, A]) → F
  8. Cylinder((0, 0, 0), (0, 0, z(D)), x(D)) → b, c, d, f
  9. Cylinder((0, 0, z(D)), (0, 0, z(E)), x(E)) → g, h, k, i
  10. Cylinder((0, 0, z(E)), (0, 0, z(F)), x(F)) → j, p, q, l