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Visualizing Solids of Revolution and Volumes by Lila Roberts (2)

Visualizing Solids of Revolution and Volumes by Lila Roberts (2)
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2016-01-09 01:58
FunctionCoordinate GeometrySolid GeometryCalculusIntegral
In collections Visualizing Solids of Revolution and Volumes
This example demonstrates the solid of revolution generated by revolving the region bounded by f(x)=x², the x-axis, and x=4. It covers core math concepts like volume of solids, integration, and coordinate geometry. Construction uses GeoGebra commands such as CurveCartesian, Polygon, Surface, curverev, and washerpolyrev to visualize 3D shapes and washer method. Ideal for high school and calculus students learning volume calculations and 3D graphing.

GeoGebra Commands & Parameters

  1. CurveCartesian(t, 0, t^(2), t, 0, 2) → fncurve
  2. Polygon((1, 0, 0), (1.2, 0, 0), (1.2, 0, 1), (1, 0, 1)) → shellpoly, h, i, j, k
  3. Surface((t * cos(s)), (t * sin(s)), t^(2), t, 0, 2, s, 0, theta) → curverev
  4. Polygon((1, 0, 1), (2, 0, 1), (2, 0, 1.2), (1, 0, 1.2)) → washerpoly, r, s, t, a_1
  5. Polygon((cos(theta), sin(theta), 0), ((1.2 * cos(theta)), (1.2 * sin(theta)), 0), ((1.2 * cos(theta)), (1.2 * sin(theta)), 1), (cos(theta), sin(theta), 1)) → shellpolyrev, l, m, n, p
  6. Polygon((cos(theta), sin(theta), 1), ((2 * cos(theta)), (2 * sin(theta)), 1), ((2 * cos(theta)), (2 * sin(theta)), 1.2), (cos(theta), sin(theta), 1.2)) → washerpolyrev, b_1, c_1, d_1, e_1
  7. CurveCartesian((t * cos(theta)), (t * sin(theta)), t^(2), t, 0, 2) → fncurverev
  8. CurveCartesian(2, 0, t, t, 0, 4) → vertcurve
  9. CurveCartesian((2 * cos(theta)), (2 * sin(theta)), t, t, 0, 4) → vertcurverev
  10. CurveCartesian(t, 0, 0, t, 0, 2) → horizaxis
  11. CurveCartesian((t * cos(theta)), (t * sin(theta)), 0, t, 0, 2) → horizaxisrev
  12. Surface((t * cos(s)), (t * sin(s)), 0, t, 0, 2, s, 0, theta) → horizaxisrev_1
  13. Surface((2 * cos(s)), (2 * sin(s)), t, t, 0, 4, s, 0, theta) → verticalrev
  14. Surface(cos(s), sin(s), t^(2), t, 0, 1, s, 0, theta) → f
  15. Surface((1.2 * cos(s)), (1.2 * sin(s)), t^(2), t, 0, 1, s, 0, theta) → g
  16. Surface((r * cos(s)), (r * sin(s)), 0, r, 0.5, 0.7, s, 0, theta) → o
  17. Surface(cos(s), sin(s), t, t, 1, 1.2, s, 0, theta) → w
  18. Surface((t * cos(s)), (t * sin(s)), 1, t, 1, 1.2, s, 0, theta) → v
  19. Surface((t * cos(s)), (t * sin(s)), 1.2, t, 1, 2, s, 0, theta) → u
  20. Surface((t * cos(s)), (t * sin(s)), 0, t, 1, 1.2, s, 0, theta) → shellaxisrev
  21. Surface((r * cos(s)), (r * sin(s)), 1, r, 1, 1.2, s, 0, theta) → q
  22. Surface((2 * cos(s)), (2 * sin(s)), t, t, 1, 1.2, s, 0, theta) → b