MathPlotAI Logo MathPlotAI

Example of Volume with Known Cross Sections Project

Example of Volume with Known Cross Sections Project
Loading the math board and drawing, please wait…
2019-05-01 02:34
FunctionSequenceSolid Geometry
This example demonstrates the calculation of volume with known cross sections, involving concepts such as cones, trapezoids, congruence, standard deviation, and cubes. Using GeoGebra commands like Polygon and Sequence, complex geometric shapes can be constructed. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  1. Polygon((X, f(X), 0), (X, f(X), f(X) - g(X)), (X, g(X), f(X) - g(X)), (X, g(X), 0)) → poly1, a, b, c, d
  2. Sequence(Polygon[(((k * X)) / n, f(((k * X)) / n), 0), (((k * X)) / n, f(((k * X)) / n), f(((k * X)) / n) - g(((k * X)) / n)), (((k * X)) / n, g(((k * X)) / n), f(((k * X)) / n) - g(((k * X)) / n)), (((k * X)) / n, g(((k * X)) / n), 0)], k, 1, n) → list1
  3. Sequence(CircumcircleArc[((k * X / n), f((k * X / n)), 0), ((k * X / n), (f((k * X / n)) + g((k * X / n))) / 2, (f((k * X / n)) - g((k * X / n))) / 2), ((k * X / n), g((k * X / n)), 0)], k, 1, n) → list3
  4. Sequence(Polygon[((k * X / n), f((k * X / n)), 0), ((k * X / n), (f((k * X / n)) + g(((k * X)) / n)) / 2, (sqrt(3) * (f((k * X / n)) - g((k * X / n))) / 2)), ((k * X / n), g((k * X / n)), 0)], k, 1, n) → list2