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Visualizing Solids of Revolution and Volumes by Lila Roberts (3)

Visualizing Solids of Revolution and Volumes by Lila Roberts (3)
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2016-01-03 08:43
FunctionSolid GeometryCalculus
This GeoGebra applet demonstrates the solid of revolution generated by revolving the region bounded by y=x^2, the x-axis, and the y-axis around the x-axis. Key mathematical concepts include functions, solid geometry, and calculus. Using commands like CurveCartesian, Surface, and Polygon, the applet constructs the image of the solid. Suitable for high school mathematics 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