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Visualizing Solids of Revolution and Volumes by Lila Roberts

Visualizing Solids of Revolution and Volumes by Lila Roberts
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2016-01-09 01:23
Solid GeometryCalculusIntegral
In collections Visualizing Solids of Revolution and Volumes
This GeoGebra applet visualizes the solid of revolution generated by revolving the region bounded by the y-axis, y=4, and f(x)=x^2 around the y-axis. Key mathematical concepts include solids of revolution and volume calculation. Constructed using commands like CurveCartesian, Surface, and Polygon. Suitable for high school math education and learning.

GeoGebra Commands & Parameters

  1. CurveCartesian(t, 0, t^(2), t, 0, 2) → a
  2. CurveCartesian(t, 0, 4, t, 0, 2) → b
  3. Surface((t * cos(s)), (t * sin(s)), t^(2), t, 0, 2, s, 0, theta) → e
  4. CurveCartesian((t * cos(theta)), (t * sin(theta)), 4, t, 0, 2) → d
  5. Surface((t * cos(s)), (t * sin(s)), 4, t, 0, 2, s, 0, theta) → c
  6. Polygon((0.5, 0, 0.5^(2)), (0.7, 0, 0.5^(2)), (0.7, 0, 4), (0.5, 0, 4)) → poly1, h, i, j, k
  7. Surface((0.5 * cos(s)), (0.5 * sin(s)), t^(2), t, 0.5, 2, s, 0, theta) → f
  8. Surface((0.7 * cos(s)), (0.7 * sin(s)), t^(2), t, 0.5, 2, s, 0, theta) → g
  9. Polygon(((0.5 * cos(theta)), (0.5 * sin(theta)), 0.5^(2)), ((0.7 * cos(theta)), (0.7 * sin(theta)), 0.5^(2)), ((0.7 * cos(theta)), (0.7 * sin(theta)), 4), ((0.5 * cos(theta)), (0.5 * sin(theta)), 4)) → poly2, l, m, n, p
  10. Surface((r * cos(s)), (r * sin(s)), 4, r, 0.5, 0.7, s, 0, theta) → o
  11. Surface((r * cos(s)), (r * sin(s)), 0.5^(2), r, 0.5, 0.7, s, 0, theta) → q
  12. Polygon((0, 0, 2), (sqrt(2), 0, 2), (sqrt(2), 0, 2.2), (0, 0, 2.2)) → poly3, r, s, t, a_1
  13. Polygon((0, 0, 2), ((sqrt(2) * cos(theta)), sin(theta), 2), ((sqrt(2) * cos(theta)), sin(theta), 2.2), (0, 0, 2.2)) → poly4, b_1, c_1, d_1, e_1
  14. Surface((t * cos(s)), (t * sin(s)), 2, t, 0, sqrt(2), s, 0, theta) → u
  15. Surface((t * cos(s)), (t * sin(s)), 2.2, t, 0, sqrt(2), s, 0, theta) → v
  16. Surface((sqrt(2) * cos(s)), (sqrt(2) * sin(s)), t, t, 2, 2.2, s, 0, theta) → w
  17. CurveCartesian((t * cos(theta)), (t * sin(theta)), t^(2), t, 0, 2) → g_1