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Volume of Revolution by Walerij Koschkin

Volume of Revolution by Walerij Koschkin
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2015-11-16 02:20
Solid GeometryCalculusIntegral
This example demonstrates the calculation of the volume of a solid of revolution. Key mathematical concepts include solids of revolution and integration. Using GeoGebra commands such as CurveCartesian, Rotate, Sequence, and Integral, the example constructs a solid of revolution and calculates its volume. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  1. CurveCartesian(t, 2^(t / 4), 0, t, 2, 8) → b
  2. Rotate(b, c, xAxis) → b'
  3. Sequence(Cylinder[((9 * (n - 1) / m), 0), ((9 * n / m), 0), sqrt((9 * n / m))], n, 1, m) → list1_1
  4. Sum(list1_1) → d_1
  5. Integral(x, 0, 9) → e
  6. Segment((2, 0), (2, 2^(1 / 2))) → g
  7. Segment((8, 0), (8, 4)) → h
  8. Rotate(g, c, xAxis) → g'
  9. Rotate(h, c, xAxis) → h'
  10. Sequence(Cylinder[(2 + (6 * n / m), 0), (2 + (6 * (n + 1) / m), 0), 2^((2 + (6 * n / m)) / 4)], n, 0, m - 1) → list2
  11. Sequence(Cylinder[(2 + (6 * n / 50), 0), (2 + (6 * (n + 1) / 50), 0), 2^((2 + (6 * n / 50)) / 4)], n, 0, 49) → list3
  12. Sum(list2) → S1
  13. Integral((π * 2^(x / 2)), 2, 8) → V1
  14. Vector((14, -10, 10), (6, 0, 0)) → u