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Rotating a Parabola Around the y-axis

Rotating a Parabola Around the y-axis
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2014-10-30 00:36
FunctionSolid GeometryCalculusGraphing
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This example demonstrates the rotation of the parabola f(x)=4x−x² around the y-axis to form a solid of revolution. Key math concepts include solid geometry, integral calculus, function graphing, and analytical geometry. Constructed using GeoGebra commands like Circle, Point, Center, Intersect, CircumcircleArc, and Surface. Suitable for high school and above students learning about 3D shapes, calculus, and function transformations.

GeoGebra Commands & Parameters

  1. Circle(xAxis, A_1) → c
  2. Point(c) → D
  3. Center(c) → E
  4. Intersect(xAxis, yAxis) → B_1
  5. Intersect(f, xAxis, 2) → H
  6. Circle(yAxis, H) → e
  7. Point(e) → A
  8. CircumcircleArc(H, I, A) → g
  9. Surface((t * cos(u)), f(t), (t * sin(u)), t, 0, 4, u, 0, g / 4) → a

AI Drawing Prompt Reference

Draw a rotating parabola around the y-axis to form a solid of revolution. Start by plotting the x and y axes, finding their intersection point. Locate the intersection points of the function f(x)=4x−x² with the x-axis, use these points to draw circles and find their intersections with the axes. Finally, use these points to create the surface of the rotating parabola, showcasing its 3D shape and rotational effect.
The prompt above was compiled from the original drawing commands and is for reference only.