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Volume of Revolution using Disks

Volume of Revolution using Disks
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2019-06-06 04:04
FunctionTrigonometrySolid GeometryCalculusIntegral
This example demonstrates the calculation of the volume of a solid of revolution using the disk method. It involves core mathematical concepts such as integration, trigonometric functions, polynomial functions, and arithmetic operations. The construction utilizes GeoGebra commands and objects like Sequence, Rotate, Circle, Surface, Textfield, and Integral. Suitable for high school students and calculus instruction.

GeoGebra Commands & Parameters

  1. Sequence(Polygon[(a + (i * deltax), 0), (a + ((i + 1) * deltax), 0), (a + ((i + 1) * deltax), f(a + ((i + 1) * deltax))), (a + (i * deltax), f(a + ((i + 1) * deltax)))], i, 0, n - 1, 1) → list1
  2. Rotate(list1, α, y = 0) → list1'
  3. Sequence((a + (i * deltax), 0), i, 0, n, 1) → list2
  4. Sequence((a + (i * deltax), f(a + (i * deltax))), i, 1, n, 1) → list3
  5. Rotate(list3, α, y = 0) → list3'
  6. Sequence((a + (i * deltax), f(a + ((i + 1) * deltax))), i, 0, n - 1, 1) → list4
  7. Sequence(x = a + (i * deltax), i, 1, n, 1) → list6
  8. Sequence(Segment[Element[list3, i], Element[list4, i]], i, 0, n, 1) → list5
  9. Sequence(CircleSector[Element[list2, i + 1], Element[list3', i], Element[list3, i], xOyPlane], i, 1, n, 1) → list7
  10. Sequence(Cylinder[Element[list2, i], Element[list2, i + 1], f(Element[list2, i + 1])], i, 1, n, 1) → list8
  11. Sequence(Circle[Element[list2, i], f(Element[list2, i]), x = 0], i, 2, n + 1, 1) → list10
  12. Circle((a, 0), f(a + deltax), x = 0) → p
  13. Surface(q, α, xAxis) → e
  14. Textfield(f) → InputBox1
  15. Textfield(a) → InputBox2
  16. Textfield(b) → InputBox3
  17. Integral(f, a, b) → m_1
  18. Textfield(n) → InputBox4

AI Drawing Prompt Reference

Illustrate the calculation of the volume of a solid of revolution using the disk method, showing the function graph, dividing it into small rectangles, rotating each to form disks, and stacking them to create the solid. Include the integral for the total volume and label key parameters like the function, integral bounds, and number of segments.
The prompt above was compiled from the original drawing commands and is for reference only.