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Using Cylinders to Show Volume of Revolution by Andrew Hitchman

Using Cylinders to Show Volume of Revolution by Andrew Hitchman
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2017-10-19 08:32
FunctionSolid GeometryCalculusGraphing
This example dynamically demonstrates how rotating cylinders form solids of revolution, visually illustrating the geometric concept of volume integration. Key math concepts include solids of revolution, integration, function graphs, and spatial geometry. Construction highlights involve using GeoGebra commands like Function, Sequence, and Sliders to create interactive models. Suitable for high school students and math enthusiasts studying calculus and solid geometry.

GeoGebra Commands & Parameters

  1. Function((((1 / 5 * (x - 1)) * (x - 3)) * (x - 5)) + 1.3, a, b) → f
  2. Div(b - a, dx) → nsteps
  3. Sequence({QuadricSide[Cylinder[(a + (dx * k), 0), (a + (dx * (k + 1)), 0), f(a + (dx * k))]], Top[Cylinder[(a + (dx * k), 0), (a + (dx * (k + 1)), 0), f(a + (dx * k))]], Bottom[Cylinder[(a + (dx * k), 0), (a + (dx * (k + 1)), 0), f(a + (dx * k))]]}, k, a, (b - a) / dx - 1) → cylinders