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Right Circular Cylinder: GeoGebra Geometric Construction

Right Circular Cylinder: GeoGebra Geometric Construction
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2012-11-03 13:42
CircleVectorSolid GeometryTransformationGeometric Construction
In collections Surface Area of cylinders
This GeoGebra example demonstrates the construction of a right circular cylinder with adjustable radius and height, visualizing its circular bases, lateral surface, height, and three-dimensional spatial structure. Core mathematical concepts include solid geometry, circles, 3D vectors, geometric transformations (dilation and translation), congruence, and cylinder surface area and volume relationships. The model is built using GeoGebra commands Dilate, Vector, Translate, Arc, Polygon, Segment, and Midpoint, along with objects such as radius, height, points A, B, P, L, R, C, and various vectors, segments, and arcs to generate the base circle, lateral approximation, and supporting construction elements. It is designed for high school solid geometry, university analytic geometry, and introductory engineering drawing, supporting interactive 3D exploration and classroom demonstration.

GeoGebra Commands & Parameters

  1. Dilate(B, height, A) → C
  2. Vector(A, C) → u
  3. Translate(c, u) → d
  4. Translate(R, u) → D
  5. Translate(P, u) → E
  6. Translate(L, u) → F
  7. Arc(d, 0, 3.141592653589793) → e
  8. Arc(c, 3.141592653589793, 0) → f
  9. Polygon(F, D, R, L) → Q, f_1, d_1, r_1, l
  10. Segment(E, P) → a
  11. Segment(P, R) → b
  12. Midpoint(E, P) → G
  13. Midpoint(P, R) → H

AI Drawing Prompt Reference

Draw an adjustable-radius and adjustable-height right circular cylinder as a 3D schematic: create a base circle, translate it along the height vector to form the top circle, choose three points on the base circle and translate them to corresponding points on the top circle, use two semicircular arcs on the top and base circles to suggest the visible outline, connect corresponding points to form a lateral edge, a base chord, and a side quadrilateral, and mark the height vector, the midpoint of the lateral edge, and the midpoint of the base chord to show the circular bases, lateral surface, and spatial structure.
The prompt above was compiled from the original drawing commands and is for reference only.