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Box Volume Calculation by Miguel Bayona

Box Volume Calculation by Miguel Bayona
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2018-10-06 22:24
FunctionSolid GeometryCalculusDerivative
This example demonstrates dynamically how sliding the base length and height illustrates the volume change of a rectangular box; core math concepts include volume formula, rectangle area, derivative application, cylinder volume, and limit theory; GeoGebra commands used in construction are polygon, orthogonal line, intersection, and segment; suitable for high school solid geometry and calculus teaching, visually explaining the relationship between volume and dimensions.

GeoGebra Commands & Parameters

  1. Polygon(pts) → sheet
  2. OrthogonalLine(P, xAxis) → g
  3. Intersect(g, xAxis) → A
  4. Segment(P, A) → h
  5. OrthogonalLine(P, yAxis) → i
  6. Intersect(i, yAxis) → B
  7. Segment(P, B) → j
  8. Polygon((a, a, 0), (a, a, a), (W - a, a, a), (W - a, a, 0)) → front, k, l, m, n
  9. Polygon((W - a, a, 0), (W - a, a, a), (W - a, L - a, a), (W - a, L - a, 0)) → rightSide, p, q, r, s
  10. Polygon((W - a, L - a, 0), (W - a, L - a, a), (a, L - a, a), (a, L - a, 0)) → back, t, b, c, d
  11. Polygon((a, L - a, 0), (a, L - a, a), (a, a, a), (a, a, 0)) → leftSide, e, f_1, g_1, h_1
  12. Polygon((a, a, 0), (W - a, a, 0), (W - a, L - a, 0), (a, L - a, 0)) → bottom, i_1, j_1, k_1, l_1
  13. Segment((a, 0), (W - a, 0)) → m_1

AI Drawing Prompt Reference

Draw a three-dimensional rectangular box volume demonstration with adjustable parameters. In the center shows a rectangular box composed of six rectangular faces: bottom, front, right, back, left and top. The box height is dynamically represented by a vertical line segment from a draggable point P on the bottom face to one side, with another perpendicular segment showing one direction of the base. The box dimensions are controlled by parameters W for width, L for length, and a for both height and offset distance from each edge, creating an inner box of size (W-2a)×(L-2a)×a. At the bottom there is also a line segment parallel to the x-axis with length W-2a, used to visually demonstrate how the rectangular box volume changes with its dimensions.
The prompt above was compiled from the original drawing commands and is for reference only.