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Visualizing Solids of Revolution and Volumes

Visualizing Solids of Revolution and Volumes
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2016-01-09 03:26
FunctionSolid Geometry
In collections Visualizing Solids of Revolution and Volumes
This applet demonstrates the solid of revolution generated by revolving the region bounded by f(x)=√x and g(x)=x around the x-axis. Key mathematical concepts include solids of revolution and volume calculation. It uses commands like Polygon, CurveCartesian, and Surface in GeoGebra. Suitable for high school math education, it helps students understand the process of generating solids of revolution and calculating their volumes.

GeoGebra Commands & Parameters

  1. Polygon((0.5^(2), 0, 0.5), (0.5^(2), 0, 0.6), (sqrt(0.5), 0, 0.6), (sqrt(0.5), 0, 0.5)) → washerpoly, e, f, g, h
  2. Polygon(((0.5 * cos(theta)), (0.5 * sin(theta)), 0.5^(2)), ((0.6 * cos(theta)), (0.6 * sin(theta)), 0.5^(2)), ((0.6 * cos(theta)), (0.6 * sin(theta)), sqrt(0.5)), ((0.5 * cos(theta)), (0.5 * sin(theta)), sqrt(0.5))) → shellpolyrev, a, b, c, d
  3. Polygon(((0.5^(2) * cos(theta)), (0.5^(2) * sin(theta)), 0.5), ((0.5^(2) * cos(theta)), (0.5^(2) * sin(theta)), 0.6), ((sqrt(0.5) * cos(theta)), (sqrt(0.5) * sin(theta)), 0.6), ((sqrt(0.5) * cos(theta)), (sqrt(0.5) * sin(theta)), 0.5)) → washerpolyrev, i, j, k, l
  4. CurveCartesian(t, 0, sqrt(t), t, 0, 1) → topcurve
  5. CurveCartesian((t * cos(theta)), (t * sin(theta)), t^(2), t, 0, 1) → fncurverev
  6. CurveCartesian(t, 0, t^(2), t, 0, 1) → fncurve
  7. CurveCartesian((t * cos(theta)), (t * sin(theta)), sqrt(t), t, 0, 1) → topcurverev_1
  8. Surface((0.5 * cos(s)), (0.5 * sin(s)), t, t, 0.5^(2), sqrt(0.5), s, 0, theta) → shellinsiderev
  9. Surface((0.6 * cos(s)), (0.6 * sin(s)), t, t, 0.5^(2), sqrt(0.5), s, 0, theta) → shelloutsiderev
  10. Surface((t * cos(s)), (t * sin(s)), 0.5^(2), t, 0.5, 0.6, s, 0, theta) → shellbottomrev
  11. Surface((t * cos(s)), (t * sin(s)), t^(2), t, 0, 1, s, 0, theta) → bottomcurverev
  12. Surface((t * cos(s)), (t * sin(s)), sqrt(t), t, 0, 1, s, 0, theta) → topcurverev
  13. Surface((t * cos(s)), (t * sin(s)), 0.5, t, 0.5^(2), sqrt(0.5), s, 0, theta) → washerbottom
  14. Surface((t * cos(s)), (t * sin(s)), 0.6, t, 0.5^(2), sqrt(0.5), s, 0, theta) → washertop
  15. Surface((sqrt(0.5) * cos(s)), (sqrt(0.5) * sin(s)), t, t, 0.5, 0.6, s, 0, theta) → washeroutside
  16. Surface((0.5^(2) * cos(s)), (0.5^(2) * sin(s)), t, t, 0.5, 0.6, s, 0, theta) → washerinside
  17. Surface((t * cos(s)), (t * sin(s)), sqrt(0.5), t, 0.5, 0.6, s, 0, theta) → shelltoprev
  18. Polygon((0.5, 0, 0.5^(2)), (0.6, 0, 0.5^(2)), (0.6, 0, sqrt(0.5)), (0.5, 0, sqrt(0.5))) → shellpoly, p, q, r, s