MathPlotAI Logo MathPlotAI

Surface Formed by Rotating a Parabola Around the y-Axis

Surface Formed by Rotating a Parabola Around the y-Axis
Loading the math board and drawing, please wait…
2014-01-29 04:07
FunctionCoordinate GeometrySolid Geometry
In collections BC Calculus
This example demonstrates the surface formed by rotating the part of the function f(x)=-(x-1)(x-4) above the x-axis around the y-axis. Key mathematical concepts include functions, solid geometry, and coordinate geometry. It uses commands like CurveCartesian, Surface, and Point in GeoGebra. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  1. Surface((u * cos(v)), f(u), (u * sin(v)), u, 1, 4, v, 0, 6.28319) → a
  2. Circle(yAxis, (1, 0, 0)) → c
  3. Point(c) → A
  4. CurveCartesian((t * cos(acos(x(A)))), f(t), (t * sin(asin(z(A)))), t, -1, 6) → b
  5. Circle(yAxis, (4, 0, 0)) → d

AI Drawing Prompt Reference

Draw a surface formed by rotating the part of the function f(x)=-(x-1)(x-4) above the x-axis around the y-axis, showing the y-axis and two circles passing through points (1,0,0) and (4,0,0), and a curve connecting these circles to illustrate the cross-section of the rotating paraboloid.
The prompt above was compiled from the original drawing commands and is for reference only.