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Volume of a Cylinder Side

Volume of a Cylinder Side
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2018-04-05 22:39
TrigonometrySolid GeometryCalculusParametric EquationGeometric Construction
This example demonstrates how to calculate the volume of a cylinder side using parametric curves and geometric transformations. It involves core math concepts like volume calculation, equilateral triangles, trigonometric functions, scatter plots, and geometric transformations. Constructed using GeoGebra commands such as Point, Circle, Intersect, Polygon, CircleSector, Textfield, OrthogonalLine, Segment, If, etc. Suitable for high school and above students learning applications of solid geometry and parametric equations.

GeoGebra Commands & Parameters

  1. Point(xAxis) → A
  2. Circle(A, 20) → c
  3. Intersect(c, f, 1) → B
  4. Intersect(c, f, 2) → C
  5. Polygon(B, A, C) → t1, c_1, b, a
  6. CircleSector(A, B, C) → d
  7. Textfield(l) → InputBox1
  8. Textfield(r) → InputBox2
  9. OrthogonalLine(A, f) → i
  10. Intersect(f, i) → D
  11. Intersect(c, i, 2) → E
  12. Segment(D, E) → j
  13. Textfield(h) → InputBox3
  14. If(h ≟ 0, (r^(2) * 3.14159), If[h ≟ (2 * r), 0, If[h < r, F_1, F_2]]) → Flatarmál
  15. Circle((0, 0), 20) → k