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Disk & Washer Method for Volumes

Disk & Washer Method for Volumes
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2019-11-20 20:46
FunctionSolid GeometryCalculusIntegralGeometric Construction
This example demonstrates the calculation of volumes of solids using the disk and washer methods in calculus. It involves core concepts such as integral computation, volume formulas for rotated solids, and geometric transformations of function graphs. Key GeoGebra commands used include Textfield, Vector, IntegralBetween, Surface, and Sequence to visualize functions, integration regions, surfaces, and animations. Suitable for high school students and calculus learners to understand volume calculation techniques.

GeoGebra Commands & Parameters

  1. Textfield(f) → InpF
  2. Vector((xc, 0, 0), (xc, f(xc), 0)) → RfVec
  3. Textfield(g) → InpG
  4. IntegralBetween(f, g, xa, xb) → BaseRegion
  5. Vector((xc, 0, 0), (xc, g(xc), 0)) → RgVec
  6. Surface(If[xa ≤ x ≤ xb, f], (2 * π), kline) → FSurf
  7. Surface(If[xa ≤ x ≤ xb, g(x)], (2 * π), kline) → GSurf
  8. Surface(u, ((((1000 * (g(u + 0.001) - f(u))) * (u - xc)) + f(u) - k) * cos(v)) + k, ((((1000 * (g(u + 0.001) - f(u))) * (u - xc)) + f(u) - k) * sin(v)), u, xc, xc + 0.001, v, 0, revolve) → Washer
  9. Sequence(Surface[u, ((((1000 * (g(u + 0.001) - f(u))) * (u - ((i * dx) + xa))) + f(u) - k) * cos(v)) + k, ((((1000 * (g(u + 0.001) - f(u))) * (u - ((i * dx) + xa))) + f(u) - k) * sin(v)), u, (i * dx) + xa, (i * dx) + xa + 0.001, v, 0, revolve], i, 0, n, 1) → RfSolid
  10. Textfield(xa) → InpA
  11. Textfield(xb) → InpB