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Volume and Surface Area of Box with Square Base

Volume and Surface Area of Box with Square Base
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2012-07-03 09:35
FunctionSolid GeometryCalculusGeometric ConstructionSlider Animation
This example demonstrates how the volume and surface area of a box with a square base change as the side length varies. Key math concepts include volume and surface area formulas, functional relationships, and variable dependencies. GeoGebra commands like Vector, Polygon, Translate, and Distance are used to construct the box, with a slider for dynamic side length adjustment. Suitable for high school students learning geometric calculations and function modeling.

GeoGebra Commands & Parameters

  1. Vector(E, F) → u
  2. Polygon(A, B, 4) → poly1, a, b, c, d, C, D
  3. Translate(B, u) → B'
  4. Translate(C, u) → C'
  5. Translate(D, u) → D'
  6. Translate(A, u) → A'
  7. Polygon(A', B', C', D') → poly2, a', b', c', d'
  8. Polygon(C, C', B', B) → poly3, c_1, c'_1, b'_1, b_1
  9. Polygon(A, A', B', B) → poly4, a_1, a'_1, b'_2, b_2
  10. Polygon(A, D, D', A') → poly5, a_2, d_1, d'_1, a'_2
  11. Polygon(D, C, C', D') → poly6, d_2, c_2, c'_2, d'_2
  12. Distance(B, B') → distanceBB'
  13. Distance(A, B) → distanceAB