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Using Cylinders to Show Volume of Revolution by Lew W. S.

Using Cylinders to Show Volume of Revolution by Lew W. S.
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2016-01-05 18:46
FunctionSolid GeometryCalculusIntegral
In collections Volume of Revolution
This example dynamically demonstrates how rotating cylinders form volumes of revolution, visually illustrating the geometric meaning of integral concepts. Core math concepts include volume of revolution, integral, function graphing, and geometric properties of cylinders. Construction highlights involve using GeoGebra commands like Function, Div, and Sequence to show variations in cylinder height and division count via slider animations, suitable for high school calculus and solid geometry learners.

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