For a positive constant $c,$ in cylindrical coordinates $(r,\theta,z),$ find the shape described by the equation
\[r = c.\](A) Line
(B) Circle
(C) Plane
(D) Sphere
(E) Cylinder
(F) Cone

Enter the letter of the correct option.
In cylindrical coordinates, $r$ denotes the distance between a point and the $z$-axis.  So if this distance is fixed, then we obtain a cylinder.  The answer is $\boxed{\text{(E)}}.$

[asy]
import three;
import solids;

size(180);
currentprojection = perspective(6,3,6);
currentlight = (1,1,2);

draw((0,-1,1)--(0,-2,1));
draw(surface(cylinder(c = (0,0,0),r = 1,h = 2)),gray(0.99));
draw((1,0,1)--(2,0,1));
draw((0,1,1)--(0,2,1));
draw((0,0,1.3)--(0,0,3));
draw((0,0,2)--(Cos(45),Sin(45),2));

label("$c$", (0.5*Cos(45),0.5*Sin(45),2), NE, white);
label("$r = c$", (0.4,0.6,-0.5), SE);
[/asy]