Surface in Cylindrical Coordinates
Loading the math board and drawing, please wait…
This example demonstrates the process and effect of drawing a surface in cylindrical coordinates. Key math concepts include cylindrical coordinates, integral calculus, surface area, volume, and 3D vectors. It uses GeoGebra's Surface command to plot the surface, involving objects like function f, equation ec1, and parameters a and b. Suitable for high school and above students learning calculus, solid geometry, and 3D graphing.
GeoGebra Commands & Parameters
Surface((u * cos(v)), (u * sin(v)) + 1, 3 - u^(2) - ((2 * u) * sin(v)), u, 0, 1, v, 0, (2 * π)) → aSurface(cos(v), sin(v) + 1, (u * (2 - (2 * sin(v)))), u, 0, 1, v, 0, (2 * π)) → b
AI Drawing Prompt Reference
Draw a surface in cylindrical coordinates, consisting of two parts. The first part has parametric equations (u * cos(v), u * sin(v) + 1, 3 - u^2 - (2 * u * sin(v))), with u ranging from 0 to 1 and v from 0 to 2π. The second part has parametric equations (cos(v), sin(v) + 1, u * (2 - 2 * sin(v))), with u ranging from 0 to 1 and v from 0 to 2π.
The prompt above was compiled from the original drawing commands and is for reference only.