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Rotating a Rectangle to Form a 3D Shape

Rotating a Rectangle to Form a 3D Shape
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2016-01-28 02:36
Solid GeometryTransformationGeometric Construction
In collections Shape Rotations Shape Rotations Shape Rotations
This example demonstrates the 3D shape formed by rotating a rectangle around an axis. Key mathematical concepts include solid geometry and rotation. It uses commands like Polygon, Cylinder, and Rotate in GeoGebra. Suitable for middle school and above students learning solid geometry.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → A
  2. Point(yAxis) → B
  3. Point(xAxis) → C
  4. OrthogonalLine(B, yAxis) → a
  5. OrthogonalLine(C, xAxis) → b
  6. Intersect(a, b) → D
  7. Polygon(B, D, C, A) → poly1, b_1, d, c, a_1
  8. Cylinder(A, B, c) → e, f, g, h
  9. Circle(A, c, yAxis) → k
  10. Circle(B, c, yAxis) → p
  11. Rotate(B, (-r), yAxis) → B'
  12. Rotate(D, (-r), yAxis) → D'
  13. Rotate(C, (-r), yAxis) → C'
  14. Rotate(A, (-r), yAxis) → A'
  15. Polygon(B', D', C', A') → poly1', b', d', c', a'

AI Drawing Prompt Reference

Draw a 3D shape formed by rotating a rectangle around the y-axis. First, draw the four vertices of the rectangle, then create a rectangle with these points. Next, draw a cylinder with A and B as the base, and draw circles with A and B as the diameter. Finally, rotate the rectangle -90 degrees around the y-axis to form a new rectangle.
The prompt above was compiled from the original drawing commands and is for reference only.