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Volume of Cone and Cylinder by HJ

Volume of Cone and Cylinder by HJ
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2017-02-22 05:38
Solid GeometryCalculusDerivativeGeometric Construction
This example demonstrates the calculation and visualization of the volumes of cones and cylinders. It involves core mathematical concepts such as volume formulas, similar triangles, derivatives, and conditional probability. The construction uses GeoGebra commands and objects like PointIn, Segment, Cylinder, Cone, and Volume. Suitable for high school students and math enthusiasts exploring solid geometry and calculus.

GeoGebra Commands & Parameters

  1. PointIn(Sphere[A, CylinderHeight]) → B
  2. Segment(A, B) → f
  3. Cylinder(A, B, CylinderRadius) → a, c, d, b
  4. PointIn(Sphere[C, ConeHeight]) → D
  5. Segment(C, D) → g
  6. Cone(C, D, ConeRadius) → e, h, i
  7. PointIn(b) → Pointb_1
  8. PointIn(b) → Pointb_2
  9. PointIn(i) → Pointi_1
  10. PointIn(b) → Pointb_3
  11. Volume(a) → volumea
  12. PointIn(b) → Pointb
  13. Volume(e) → volumee
  14. PointIn(i) → Pointi