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Volume of Solid of Revolution about x-axis

Volume of Solid of Revolution about x-axis
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2018-05-13 19:06
FunctionSolid GeometryCalculusIntegralGraphing
This example demonstrates the calculation of the volume of a solid formed by revolving a plane region around the x-axis using integral calculus. It involves core math concepts like integration, volume of solids of revolution, and function visualization. Constructed with GeoGebra commands like Integral, Surface, and Textfield for input and display. Ideal for high school and college students learning calculus and geometry applications.

GeoGebra Commands & Parameters

  1. Textfield(f) → InputBox1
  2. Integral(f, a, b) → c
  3. Surface(t, (f(t) * cos(u)), (f(t) * sin(u)), t, a, b, u, 0, 6.28319) → g
  4. Textfield(a) → InputBox2
  5. Textfield(b) → InputBox3
  6. Integral(h, a, b) → vol
  7. FractionText(voldpi) → text2

AI Drawing Prompt Reference

Draw a function graph and display the volume of the solid formed by revolving the region around the x-axis, requiring input for the function expression and integration bounds, calculate the volume using integration, and show the 3D solid of revolution, while displaying the calculation result and input parameters on the interface.
The prompt above was compiled from the original drawing commands and is for reference only.