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Example 2: Constructing a Cylinder Surface with a Piecewise Function and Demonst

Example 2: Constructing a Cylinder Surface with a Piecewise Function and Demonst
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2012-07-10 21:33
FunctionCalculusIntegralGeometric ConstructionSlider Animation
In collections CCSS IP Math I Unit 4 Lesson 2
①This example demonstrates how to construct a cylinder surface defined by a piecewise function using GeoGebra and illustrates volume approximation via upper and lower Riemann sums. ②Key mathematical concepts include piecewise functions, cylindrical surfaces, the idea of upper and lower Riemann sums, and the calculus principle of approximating continuous quantities with discrete sums. ③Construction highlights: using the Corner command to place vertices, Sequence to generate points, Segment to draw edges, Polygon to render the cylindrical surface, Textfield and Slider for parameter control, and VerticalText for labeling. ④Suitable for high‑school or first‑year university students in calculus, analytic geometry, or mathematical modeling courses covering solid geometry and integral concepts.

GeoGebra Commands & Parameters

  1. Corner(2) → Corn2
  2. Corner(3) → Corn3
  3. Textfield(A2) → InA2
  4. Textfield(A3) → InA3
  5. Textfield(A4) → InA4
  6. Textfield(A5) → InA5
  7. Textfield(A6) → InA6
  8. Textfield(A7) → InA7
  9. Textfield(A8) → InA8
  10. Textfield(A9) → InA9
  11. Textfield(B9) → InB9
  12. Textfield(B8) → InB8
  13. Textfield(B7) → InB7
  14. Textfield(B6) → InB6
  15. Textfield(B5) → InB5
  16. Textfield(B4) → InB4
  17. Textfield(B3) → InB3
  18. Textfield(B2) → InB2
  19. Sequence(Segment[(10.5, 100 + (80 * j)), (14, 100 + (80 * j))], j, 0, 8) → LnList
  20. Sequence(Segment[(14, 100 + (80 * j)), (16, 100 + (80 * j))], j, 0, 8) → LnList3
  21. Sequence(Segment[(10.5 + (1.75 * j), 100), (10.5 + (1.75 * j), 860)], j, 0, 2) → LnList2
  22. Segment((10.5, 860), (14, 860)) → Top1
  23. Segment((14, 860), (16, 860)) → Top2
  24. Segment((16, 100), (16, 860)) → Side1
  25. Polygon((0.5 * Corner[1]) + (0.5 * Corner[2]), Corner[2], Corner[3], (0.5 * Corner[3]) + (0.5 * Corner[4])) → poly1, b, c, d, e
  26. VerticalText("Students") → Students

AI Drawing Prompt Reference

Draw a cylindrical surface defined by a piecewise function and illustrate volume approximation using upper and lower Riemann sums. Include adjustable sliders and text fields to control the function parameters. The cylinder side consists of a series of parallel rectangular strips forming a grid, with top and bottom edges closed by line segments and vertical boundaries on the sides. Add a vertical label “Students” on the right.
The prompt above was compiled from the original drawing commands and is for reference only.