Cone and inscribed cylinder - part 2
- Autor:
- Andreas Lindner
- Thema:
- Analysis, Kegel, Zylinder, Oberfläche
A rotation cylinder with radius r and height h is to be inscribed in a cone with radius R and height H.
Find the dimensions of the cylinder when the volume is maximum.
This example can be interpreted in the following way:
The volume of the inscribed cylinder V(r,h) = r²π·h is a function with 2 variables and can be displayed as a surface.
The additional condition can be written as and displayed as a plane using the variables r and h (without a third variable and therefore perpendicular to the xOy plane). The local maximum oh the intersecting curve of the surface V(r,h) and the plane gives the maximum volume of the inscribed cylinder.
Exercise
Use slider r to move point P and find the maximum of the volume of the inscribed cylinder.
Andreas Lindner