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Volume of Two Cones Cut from the Same Circle

Volume of Two Cones Cut from the Same Circle
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2016-02-19 19:53
CircleGeometric ConstructionSlider Animation
This example demonstrates the volumes of two cones cut from the same circle. Key mathematical concepts include circle, cone, and volume. Using GeoGebra commands such as Circle, Intersect, Point, Angle, and Cone, the construction of cones and the calculation of their volumes are illustrated. Suitable for middle school and above students or teachers.

GeoGebra Commands & Parameters

  1. Circle(A, 1) → circle
  2. Intersect(circle, xAxis, 2) → B
  3. Point(circle) → C
  4. Angle(B, A, C) → θ_1
  5. Angle(C, A, B) → θ_2
  6. CircleArc(A, B, C) → c_1
  7. CircleArc(A, C, B) → c_2
  8. OrthogonalLine(E, xOyPlane) → a
  9. OrthogonalLine(D, xOyPlane) → b
  10. Sphere(F, 1) → c
  11. Sphere(G, 1) → d
  12. Intersect(a, d) → H, I
  13. Intersect(b, c) → J, K
  14. Cone(D, K, r_1) → e, f, g
  15. Cone(E, I, r_2) → h, k, i
  16. Segment(C, A) → j
  17. CircleSector(A, B, C) → p
  18. CircleSector(A, C, B) → q
  19. LaTeX(θ_1, true, true) → text1
  20. LaTeX(Vol, true, true) → text2