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Fraction of a Cylinder

Fraction of a Cylinder
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2016-02-28 02:57
FunctionSolid GeometryGeometric Construction
This example demonstrates the fraction of a cylinder. It involves concepts of cylinder geometry and fractions. Using the GeoGebra command Surface, users can construct the fraction of a cylinder. Suitable for middle and high school students learning solid geometry and fraction applications.

GeoGebra Commands & Parameters

  1. Surface((((v * r) * f(u)) * cos(u)), (((v * r) * f(u)) * sin(u)), h1 / 2, u, 0, (2 * π), v, 0, 1) → c
  2. Surface(((r * f(u)) * cos(u)), ((r * f(u)) * sin(u)), v, u, 0, (2 * π), v, ((-h1)) / 2, h1 / 2) → a
  3. Surface(((r * g(u)) * cos(u)), ((r * g(u)) * sin(u)), v, u, 0, (2 * π), v, ((-h2)) / 2, h2 / 2) → b
  4. Surface((((v * r) * f(u)) * cos(u)), (((v * r) * f(u)) * sin(u)), ((-h1)) / 2, u, 0, (2 * π), v, 0, 1) → cc
  5. Surface((((v * r) * g(u)) * cos(u)), (((v * r) * g(u)) * sin(u)), h2 / 2, u, 0, (2 * π), v, 0, 1) → d
  6. Surface((((v * r) * g(u)) * cos(u)), (((v * r) * g(u)) * sin(u)), ((-h2)) / 2, u, 0, (2 * π), v, 0, 1) → e

AI Drawing Prompt Reference

Draw a three-dimensional solid representing a fraction of a cylinder, composed of two stacked segments with different heights. The shape includes a curved lateral surface formed by rotation, and circular top and bottom faces. The lower segment has a smaller height, while the upper segment is taller, illustrating a proportional division. Construct the lateral surface first, then add the circular end caps, ensuring smooth continuous surfaces. The overall form is a partial cylinder with visible curved sides and flat circular bases.
The prompt above was compiled from the original drawing commands and is for reference only.