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Using Cylinders to Show Volume of Revolution

Using Cylinders to Show Volume of Revolution
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2019-04-06 04:15
FunctionSolid GeometryCalculusGraphing
This example dynamically demonstrates how rotating a cylinder forms a volume of revolution, visually illustrating the geometric meaning of integral concepts. Core math concepts include volume of revolution, integral, function graphing, and geometric transformation. Construction highlights involve GeoGebra commands like Function, Div, and Sequence to show the change in cylinder height and base area through slider animations, suitable for high school calculus teaching and volume calculation visualization.

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