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Vertical Rectangles Rotated About the X-axis

Vertical Rectangles Rotated About the X-axis
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2017-10-08 08:20
FunctionSolid GeometryCalculus
This example demonstrates the solid of revolution formed by rotating vertical rectangles about the x-axis. It involves core mathematical concepts such as solid geometry, rotation, integration, and function graphing. The construction uses GeoGebra commands like Point, Sequence, Rotate, and Textfield to create points, sequences, rotations, and text fields. Suitable for high school and above students learning about volume of solids of revolution and function graphing.

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. Sequence(Cylinder[(a + ((k - 1) * w), 0), (a + (k * w), 0), f(a + (k * w))], k, 1, n) → discs
  5. Rotate(rects, θ, xAxis) → rects'
  6. Textfield(f) → InputBox1