MathPlotAI Logo MathPlotAI

Volume of Cone-Cylinder

Volume of Cone-Cylinder
Loading the math board and drawing, please wait…
2017-10-10 11:10
Solid GeometryCalculusGeometric Construction
This example demonstrates the calculation of the volume of a combined cone-cylinder solid. It involves core mathematical concepts such as volume formulas in solid geometry and spatial geometric relationships. The construction utilizes GeoGebra commands and objects like OrthogonalLine, Point, Cone, OrthogonalPlane, IntersectPath, Corner, Cylinder, Volume, PointIn, Name, Distance, Midpoint, DynamicCoordinates, and Intersect. It is suitable for high school geometry teaching and volume calculation practice.

GeoGebra Commands & Parameters

  1. OrthogonalLine(A, xOyPlane) → f
  2. Point(f) → B
  3. Cone(A, B, 5) → b, b_2, b_3
  4. Point(f) → C
  5. OrthogonalPlane(C, f) → a
  6. IntersectPath(a, b) → c
  7. Corner(c)
  8. Point(c) → D
  9. Cylinder(C, A, Distance[D, C]) → d, e, g, h
  10. Volume(b) → volumeb
  11. PointIn(b_3) → Pointb3
  12. Volume(d) → volumed
  13. PointIn(h) → Pointh
  14. Name(d) → A1
  15. Distance(C, A) → distanceCA
  16. Midpoint(C, A) →
  17. DynamicCoordinates(E, Distance[C, A], d) → F
  18. OrthogonalLine(F, yAxis) → i
  19. OrthogonalLine(F, xAxis) → j
  20. Intersect(i, yAxis) → G
  21. Intersect(j, xAxis) → H
  22. Distance(B, A) → distanceBA
  23. Midpoint(B, A) →
  24. Distance(B, A) → BA