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Vertical Rectangles Rotated About the Y-axis

Vertical Rectangles Rotated About the Y-axis
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2017-10-09 04:57
FunctionSolid GeometryCalculus
This example demonstrates the rotation of vertical rectangles about the y-axis to form a solid of revolution. Key math concepts include rotation, integration, solid geometry, and function graphing. It utilizes GeoGebra commands and objects like Point, Sequence, Rotate, Textfield, Append, PolyLine, and Surface to construct the rotating rectangles and visualize the resulting solid. Suitable for high school and above students to learn about the volume of solids of revolution and the application of integration.

GeoGebra Commands & Parameters

  1. Point(xAxis) → A
  2. Point(Ray[A, A + (1, 0)]) → B
  3. Sequence(Polygon[{(a + (k * w), 0), (a + (k * w), f(a + (k * w))), (a + ((k - 1) * w), f(a + (k * w))), (a + ((k - 1) * w), 0)}], k, 1, n) → rects
  4. Rotate(rects, θ, yAxis) → rects'
  5. Textfield(f) → InputBox1
  6. Append(Append[A, Sequence[(a + (floor(k) * w), f(a + (ceil(k) * w))), k, 0.5, n, 0.5]], B) → cor
  7. PolyLine(cor) → g
  8. Surface(g, (2 * π), Line[(0, 0, 0), (0, 1, 0)]) → shells