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Rate of Change - Filling a Cylinder

Rate of Change - Filling a Cylinder
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2017-04-04 19:10
FunctionSolid GeometryCalculusGeometric Construction
This example demonstrates the dynamic process of water level change in a cylinder over time as it is filled. Key math concepts include rate of change, linear equations, volume calculation, and integral concepts. GeoGebra commands and objects used in construction include Polygon, Textfield, Max, and objects like swlevel2, width2, Fill, swlevel1, height1, etc. It is suitable for high school students learning applications of calculus on rates of change and integrals, or for teaching volume changes in solid geometry.

GeoGebra Commands & Parameters

  1. Polygon(A1, (x(A1) + width1, y(A1)), (x(A1) + width1, y(A1) + height1), (x(A1), y(A1) + height1)) → polyc1edge, a1, a, b, c_1
  2. Polygon(A1, (x(A1) + width1, y(A1)), (x(A1) + width1, y(A1) + wheight1), (x(A1), y(A1) + wheight1)) → polyc1water, a1_1, d, e, f
  3. Polygon(A1, (x(A1) + width1, y(A1)), (x(A1) + width1, y(A1) + height1), (x(A1), y(A1) + height1)) → polyc1full, a1_2, g, h, i
  4. Polygon(A2, (x(A2) + width2, y(A2)), (x(A2) + width2, y(A2) + height2), (x(A2), y(A2) + height2)) → polyc2edge, a2, j, k, l
  5. Polygon(A2, (x(A2) + width2, y(A2)), (x(A2) + width2, y(A2) + height2), (x(A2), y(A2) + height2)) → polyc2full, a2_1, m, n, p
  6. Polygon(A2, (x(A2) + width2, y(A2)), (x(A2) + width2, y(A2) + wheight2), (x(A2), y(A2) + wheight2)) → polyc2water, a2_2, q, r, s
  7. Textfield(swlevel1) → inputBox6
  8. Textfield(swlevel2) → inputBox7
  9. Max(((π * (width1 / 2)^(2)) * height1) - ((π * (width1 / 2)^(2)) * swlevel1), ((π * (width2 / 2)^(2)) * height2) - ((π * (width2 / 2)^(2)) * swlevel2)) → MaxWater

AI Drawing Prompt Reference

Draw two cylindrical containers with bottom widths width1 and width2, and heights height1 and height2. Draw water level lines swlevel1 and swlevel2 in each container, and fill the water area with different colors. Show the volume change of water. Finally, calculate and display the difference in water volume between the two containers.
The prompt above was compiled from the original drawing commands and is for reference only.