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Archimedes Cylinder and Sphere

Archimedes Cylinder and Sphere
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2015-11-05 04:27
FunctionSolid GeometryCalculusGeometric Construction
This example demonstrates the geometric relationship between Archimedes' cylinder and sphere, particularly the volume relationship between the sphere and the cylinder. It involves core mathematical concepts such as cylinder, sphere, exponent, indefinite integral, power functions, and differential equations. The construction uses GeoGebra commands like Intersect, Point, Cylinder, Sphere, and Segment. It is suitable for high school and above students studying solid geometry and calculus.

GeoGebra Commands & Parameters

  1. Intersect(zAxis, yAxis) → A
  2. Point(zAxis) → B
  3. Cylinder(A, B, 5) → a, c, d, b
  4. Point(zAxis) → C
  5. Sphere(C, 5) → e
  6. Point(d) → D
  7. Point(c) → E
  8. Segment(D, E) → g
  9. Segment(B, D) → f
  10. Intersect(g, b, 1) → F
  11. Segment(C, F) → h