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Washer Method Demonstration

Washer Method Demonstration
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2014-05-12 11:33
FunctionCalculusIntegral
In collections Volumes of Solids
This example demonstrates the washer method for calculating the volume of a solid of revolution. It involves core mathematical concepts like integration, functions, limits, and geometric transformations. Constructed using commands and objects such as Intersect, Segment, CurveCartesian, Textfield, and Function. Suitable for high school and above students learning about the washer method in calculus.

GeoGebra Commands & Parameters

  1. Intersect(f, h) → A, B, C
  2. Segment((b, h(b)), (b, f(b))) → j
  3. CurveCartesian(b + (f(b) - m) * sin(t°) / 100, m + (f(b) - m) * cos(t°), t, 0, a) → k
  4. CurveCartesian(b + (h(b) - m) * sin(t°) / 100, m + (h(b) - m) * cos(t°), t, 0, a) → l
  5. Segment((b + (h(b) - m) * sin(a°) / 100, m + (h(b) - m) * cos(a°)), (b + (f(b) - m) * sin(a°) / 100, m + (f(b) - m) * cos(a°))) → i
  6. CurveCartesian(b + (f(b) - m) * sin(t°) / 100, m + (f(b) - m) * cos(t°), t, 0, a) → s
  7. CurveCartesian(b + (h(b) - m) * sin(t°) / 100, m + (h(b) - m) * cos(t°), t, 0, a) → u
  8. Textfield(m) → inputBox1
  9. Textfield(initial) → inputBox2
  10. Textfield(terminal) → inputBox3
  11. CurveCartesian(t + (h(t) - m) * sin(a°) / 100, m + (h(t) - m) * cos(a°), t, initial, terminal) → c
  12. CurveCartesian(t + (f(t) - m) * sin(a°) / 100, m + (f(t) - m) * cos(a°), t, initial, terminal) → q
  13. Textfield(f) → inputBox4
  14. Textfield(h) → inputBox5
  15. CurveCartesian(terminal + (h(terminal) - m) * sin(t°) / 100, m + (h(terminal) - m) * cos(t°), t, 0, a) → e
  16. CurveCartesian(initial + (h(initial) - m) * sin(t°) / 100, m + (h(initial) - m) * cos(t°), t, 0, a) → d
  17. CurveCartesian(t + (f(t) - m) * sin(a°) / 100, m + (f(t) - m) * cos(a°), t, initial, terminal) → g
  18. CurveCartesian(t + (h(t) - m) * sin(a°) / 100, m + (h(t) - m) * cos(a°), t, initial, terminal) → o
  19. Function(-f(x) + 2 * m, initial, terminal) → g_1
  20. Function(-h(x) + 2 * m, initial, terminal) → f_1

AI Drawing Prompt Reference

Draw a demonstration of the washer method for calculating volume of revolution. Show two function curves, one upper and one lower, enclosing a region. At a point on the x-axis, draw a vertical segment between the curves representing thickness. Around this point, draw two circular arcs with radii equal to the distances to the upper and lower curves, forming a washer cross-section. Then draw the full solid of revolution from a start x-value to an end x-value, including inner and outer surfaces and circular end caps. Include input boxes for adjusting the axis height, start and end x-values, and the two function expressions.
The prompt above was compiled from the original drawing commands and is for reference only.