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Half Cylinder: Geometric Construction of a Semi-Cylinder

Half Cylinder: Geometric Construction of a Semi-Cylinder
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2018-10-23 20:09
Solid GeometryGeometric Construction
Half Cylinder demonstrates the upper half of a cylinder, illustrating volume calculations and geometric transformations. Key mathematical concepts include the volume formula of a cylinder, the constant π, and geometric transformations. Construction involves GeoGebra commands such as Segment, Semicircle, Translate, and Polygon. Suitable for middle or high school mathematics courses to enhance spatial reasoning and geometric understanding.

GeoGebra Commands & Parameters

  1. Segment(A, B) → f
  2. Semicircle(A, B, xOyPlane) → c
  3. Vector((0, 0, 0), (0, 0, 4)) → u
  4. Translate(c, u) → c'
  5. Point(c') → C
  6. Point(c') → D
  7. Polygon(A, B, D, C) → t1, g, h, i, j
  8. Surface(cos(α), sin(α), h, α, 0°, 180°, h, 0, 4) → a

AI Drawing Prompt Reference

Draw the upper half of a cylinder: start with a line segment as a diameter on the horizontal plane, construct a semicircle on it, translate that semicircle vertically by four units to create the top semicircle, connect the corresponding endpoints to form a rectangular side, and finally generate the curved surface swept by the semicircle around the vertical axis, illustrating the half‑cylinder geometry and its volume structure.
The prompt above was compiled from the original drawing commands and is for reference only.