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Volume Calculation of a Dam

Volume Calculation of a Dam
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2015-06-06 18:20
Solid GeometryCalculusIntegral
This example demonstrates how to calculate the volume of a dam using integration. Key mathematical concepts include integral calculus and solid geometry. Using GeoGebra commands such as Point, Function, Surface, etc., the shape and volume of the dam can be dynamically displayed. Suitable for high school and above students learning calculus and solid geometry.

GeoGebra Commands & Parameters

  1. Point(c) → A
  2. Function((y(A - 16) / 2116 * x^(2)) + 16, -46, 46) → g
  3. Function((y(A - 16) / 2116 * x^(2)), -46, 46) → f
  4. Surface(u, f(u) - b(w) + 8, w, u, -46, 46, w, 0, h) → s_3
  5. Surface(u, g(u) + b(w) - 8, w, u, -46, 46, w, 0, h) → s_1
  6. Surface(u, f(u) - b(z) + 8 + (w * b(z)), z, u, -46, 46, w, 0, 2) → a
  7. LaTeX(f, true, true) → Text1
  8. LaTeX(g, true, true) → Text4
  9. LaTeX(b, true, true) → Text5
  10. Surface(46, f(46) + 8 - b(w) + ((u * 2) * b(w)), w, u, 0, 1, w, 0, h) → s_2
  11. Surface(-46, f(-46) + 8 - b(w) + ((u * 2) * b(w)), w, u, 0, 1, w, 0, h) → s_4
  12. CurveCartesian(46, f(46) + 8 + b(t), t, t, 0, 24) → a_1
  13. CurveCartesian(-46, f(-46) + 8 + b(t), t, t, 0, 24) → a_2
  14. CurveCartesian(-46, f(-46) + 8 - b(t), t, t, 0, 24) → a_3
  15. CurveCartesian(46, f(46) + 8 - b(t), t, t, 0, 24) → a_4
  16. Sequence(Prism[Polygon[(46, b((k * s)) + 8, (k * s)), ((-46), b((k * s)) + 8, (k * s)), ((-46), (-b((k * s))) + 8, (k * s)), (46, (-b((k * s))) + 8, (k * s))], h / n], k, 0, n - 1) → Liste1
  17. Sum(Liste1) → V_Q

AI Drawing Prompt Reference

Draw a dam volume calculation diagram, including a parabolic base opening upwards. First, draw the parabolic functions g and f, then create the dam surfaces s_1, s_3, and s_4 using these functions. Next, draw the boundary curves a_1, a_2, a_3, and a_4. Finally, calculate the dam's volume V_Q using integration.
The prompt above was compiled from the original drawing commands and is for reference only.