MathPlotAI Logo MathPlotAI

Cavalieri's Principle with Spheres

Cavalieri's Principle with Spheres
Loading the math board and drawing, please wait…
2020-01-27 01:20
Solid GeometryCalculusGeometric Construction
This example demonstrates Cavalieri's Principle by comparing cross-sections of a sphere, cone, and cylinder. It involves core concepts like volume, geometric similarity, and integral calculus. GeoGebra commands used include OrthogonalLine, Circle, Vector, Translate, Sphere, Cylinder, Point, OrthogonalPlane, IntersectPath, and Cone. Suitable for high school geometry and calculus education to visually understand volume calculation principles.

GeoGebra Commands & Parameters

  1. OrthogonalLine(A, xOyPlane) → a
  2. Circle(A, 2, a) → c
  3. Vector(A, B) → u
  4. Translate(c, u) → c'
  5. Sphere(A, 2) → b
  6. Cylinder(B, D, 2) → d, e, f, g
  7. OrthogonalLine(F, xOyPlane) → j
  8. Point(j) → G
  9. OrthogonalPlane(G, j) → l
  10. IntersectPath(l, b) → q
  11. IntersectPath(l, d) → r
  12. Vector(A, E) → v
  13. Translate(c, v) → c'_1
  14. Cone(E, C, 2) → h, k, i
  15. IntersectPath(l, h) → p
  16. Corner(p)
  17. Vector(F, G) → w