If for example I have the circle $x^2 + y^2 = 4$ in the $x$-$y$ plane, and I want to extend it upwards into the $z$ dimension, how would I write the equation for the circular walls in terms of $z$?
2026-04-04 01:54:45.1775267685
On
What is the equation for the walls of a 3D cylinder?
155 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail At
2
There are 2 best solutions below
0
On
Actually what you wrote is for an entire cylinder of unspecified height.But to specify where it starts and ends,
the (x,y,z) surface (cylinder ) parametrization is
$$ (x = 2 \cos u, y=2 \sin u, z=v ),( 0< u< 2 \pi), ( hmin < v < hmax) $$
Where the height is between two limits.
Useful for extruded /prismatic surfaces.
The same equation will work, as for given $x_0$ and $y_0$ on the circle, for any $z$, at the vertical of $(x_0,y_0)$, $(x_0,y_0,z)$ will be on the wall, as in the figure from Quadric Surfaces:
If you really miss the $z$, try $x^2 + y^2 + 0\times z = 4$.