Cylinder Filling Demonstration

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2016-01-05 02:10

This example demonstrates the filling process of a cylinder with water as its height changes, along with related function graphs. Key mathematical concepts include cylinder volume calculation, functional relationships, geometric transformations, and data visualization. GeoGebra commands like Textfield, Polygon, and Max are used to dynamically adjust water level and dimensions via sliders. Suitable for high school geometry, function graphing, and data analysis instruction, illustrating volume formula applications and parameter effects.

GeoGebra Commands & Parameters

Textfield(width1) → inputBox1
Textfield(width2) → inputBox2
Textfield(height1) → inputBox3
Textfield(height2) → inputBox4
Polygon(A1, (x(A1) + width1, y(A1)), (x(A1) + width1, y(A1) + height1), (x(A1), y(A1) + height1)) → polyc1edge, a1, a, b, c_1
Polygon(A1, (x(A1) + width1, y(A1)), (x(A1) + width1, y(A1) + wheight1), (x(A1), y(A1) + wheight1)) → polyc1water, a1_1, d, e, f
Polygon(A1, (x(A1) + width1, y(A1)), (x(A1) + width1, y(A1) + height1), (x(A1), y(A1) + height1)) → polyc1full, a1_2, g, h, i
Polygon(A2, (x(A2) + width2, y(A2)), (x(A2) + width2, y(A2) + height2), (x(A2), y(A2) + height2)) → polyc2edge, a2, j, k, l
Polygon(A2, (x(A2) + width2, y(A2)), (x(A2) + width2, y(A2) + height2), (x(A2), y(A2) + height2)) → polyc2full, a2_1, m, n, p
Polygon(A2, (x(A2) + width2, y(A2)), (x(A2) + width2, y(A2) + wheight2), (x(A2), y(A2) + wheight2)) → polyc2water, a2_2, q, r, s
Textfield(swlevel1) → inputBox6
Textfield(swlevel2) → inputBox7
Max(π * (width1 / 2)^(2) * height1 - π * (width1 / 2)^(2) * swlevel1, π * (width2 / 2)^(2) * height2 - π * (width2 / 2)^(2) * swlevel2) → MaxWater