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Volume of Revolution: Washer Method

Volume of Revolution: Washer Method
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2020-04-21 23:45
Solid GeometryCalculusIntegral
In collections Calculus - Applications of Integrals - Areas and Volumes
This example demonstrates the Washer Method for calculating the volume of revolution. Key mathematical concepts include integration and solid geometry. Using GeoGebra commands such as Polygon, Surface, Sequence, and Rotate, the formation of the solid of revolution is dynamically illustrated. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  1. Polygon(A, B, D, C) → q1, a_1, b_1, d, c
  2. Surface(x(B), ((u * y(D)) * cos(v)), ((u * y(D)) * sin(v)), u, 0, 1, v, 0, α) → f
  3. Surface(x(A), ((u * y(D)) * cos(v)), ((u * y(D)) * sin(v)), u, 0, 1, v, 0, α) → g
  4. Sequence(Surface[a + (i * deltax) + (deltax * u), (h(a + ((i + 1) * deltax)) * cos(v)), (h(a + ((i + 1) * deltax)) * sin(v)), u, 0, 1, v, 0, α], i, 0, n - 1, 1) → L_4
  5. Sequence(Polygon[(a + (i * deltax), p(a + ((i + 1) * deltax))), (a + ((i + 1) * deltax), p(a + ((i + 1) * deltax))), (a + ((i + 1) * deltax), h(a + ((i + 1) * deltax))), (a + (i * deltax), h(a + ((i + 1) * deltax)))], i, 0, n - 1) → diffrectangles
  6. Sequence(Surface[a + (i * deltax) + (deltax * u), (p(a + ((i + 1) * deltax)) * cos(v)), (p(a + ((i + 1) * deltax)) * sin(v)), u, 0, 1, v, 0, α], i, 0, n - 1, 1) → l1
  7. Rotate(diffrectangles, α, xAxis) → diffrectangles'
  8. Textfield(h) → InputBox1
  9. Textfield(p) → InputBox2
  10. Textfield(a) → InputBox3
  11. Textfield(b) → InputBox4
  12. Textfield(n) → InputBox5
  13. Sequence(Surface[a + (i * deltax), (cos(v) * ((h(a + (i * deltax)) * u) + (p(a + (i * deltax)) * (1 - u)))), (sin(v) * ((h(a + (i * deltax)) * u) + (p(a + (i * deltax)) * (1 - u)))), u, 0, 1, v, 0, α], i, 1, n, 1) → L_2
  14. Sequence(Surface[a + ((i - 1) * deltax), (cos(v) * ((h(a + (i * deltax)) * u) + (p(a + (i * deltax)) * (1 - u)))), (sin(v) * ((h(a + (i * deltax)) * u) + (p(a + (i * deltax)) * (1 - u)))), u, 0, 1, v, 0, α], i, 1, n, 1) → L_3