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Construct a Cylinder with Sliders and Discover Its Volume

Construct a Cylinder with Sliders and Discover Its Volume
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2012-08-09 06:21
Solid GeometryGeometric ConstructionSlider Animation
In collections Surface Area and Volume Surface Area and Volume Surface Area and Volume Visual Geometry for Grade 9 Area, perimeter and volume of shapes Area, Perimeter and Volume of shapes Circumference, Area, and Volume Surface Area and Volume of basic figures Surface Area and Volume of basic figures Surface Area and Volume of basic figures
This example uses interactive sliders to let students dynamically construct a cylinder and explore how to calculate its volume. It covers the geometric properties of a cylinder, the relationship between base area and height, and the volume formula V = πr²h. Built with GeoGebra commands such as Intersect, Vector, Translate, Segment, Arc, Polygon, Root, Midpoint, and auxiliary objects (radius, control points), the cylinder is generated dynamically and the result is displayed in real time. Designed for high‑school and college students studying solid geometry and applied mathematics, it is ideal for classroom demos, problem solving, and independent inquiry.

GeoGebra Commands & Parameters

  1. Intersect(c, xAxis, 1) → A
  2. Intersect(c, xAxis, 2) → B
  3. Vector((-17, 0), (-1 * 17, b)) → u
  4. Translate(c, u) → d
  5. Translate(A, u) → C
  6. Translate(B, u) → D
  7. Segment(A, C) → e
  8. Segment(B, D) → f
  9. Arc(c, A, B) → g
  10. Polygon(C, D, B, A) → P, c_1, d_1, b_1, a_1
  11. Intersect(xAxis, yAxis) → E
  12. Segment(E, B) → h
  13. Translate(E, u) → E'
  14. Translate(B, u) → B'
  15. Segment(E', B') → i
  16. Root(32) → F
  17. Midpoint(i) → G
  18. Midpoint(e) → H

AI Drawing Prompt Reference

Draw a cylinder by adjusting the radius and height with sliders. Start by drawing a circle as the base, then create another base by translating the first one. Draw two parallel line segments as the side of the cylinder, and connect the two bases with arcs to form the side. Finally, use the sliders to dynamically adjust the cylinder's dimensions and observe the volume change.
The prompt above was compiled from the original drawing commands and is for reference only.