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Volume of a Cylinder vs Cone

Volume of a Cylinder vs Cone
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2020-08-19 16:34
FunctionSolid GeometryGeometric ConstructionSlider Animation
① This GeoGebra example demonstrates the relationship between the volumes of a cylinder and a cone, especially showing that for equal base and height, the cone's volume is one-third of the cylinder's. ② Core mathematical concepts include solid geometry, volume formulas, and dynamic parameter variation. ③ Construction uses commands such as Point, Circle, Cylinder, Cone, Volume, Translate, Vector, and Text objects, with sliders to adjust radius and height, enabling real-time volume comparison. ④ Suitable for middle and high school geometry classes, ideal for visualizing volume formulas and supporting inquiry-based learning.

GeoGebra Commands & Parameters

  1. Point({r, 0, 0}) → B
  2. Circle(zAxis, B) → c
  3. Cylinder(c, h) → a, d, b
  4. Area(c) → e
  5. Point({0, t, 0}) → A
  6. Point({0, 0, 0}) → O
  7. Vector(O, A) → u
  8. Translate(c, u) → d'
  9. Cone(d', h) → f, g, i
  10. Segment(O, B) → j
  11. Circumference(d) → circumferenced
  12. PointIn(d) → Pointd
  13. Circumference(d') → circumferenced'
  14. PointIn(d') → Pointd'
  15. Volume(a) → volumea
  16. PointIn(b) → Pointb
  17. Volume(f) → volumef
  18. PointIn(i) → Pointi
  19. Translate(C, u) → C'

AI Drawing Prompt Reference

Draw a cylinder and a cone with equal base radius and height, controlled by sliders. Display the volumes of the cylinder and cone, and label that the cone's volume is one-third of the cylinder's. The cylinder and cone should extend vertically from the center of their circular bases. The base of each is a circle, and their centers are aligned horizontally. The cone's apex is directly above the center of the cylinder's base.
The prompt above was compiled from the original drawing commands and is for reference only.