### Instruction: 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.### Response: To visualize the shape, I need to recall what cylindrical coordinates mean.
They are like polar coordinates in the $xy$-plane, but with an extra $z$-coordinate for height.
So, $r$ is the distance from the $z$-axis, $\theta$ is the angle measured counterclockwise from the positive $x$-axis, and $z$ is the height above or below the $xy$-plane.
If $r = c,$ then I have a constant distance from the $z$-axis, regardless of the values of $\theta$ and $z.$
This means that the shape is a cylinder of radius $c$ centered on the $z$-axis.
The equation does not restrict the values of $\theta$ or $z,$ so the cylinder is infinitely long and wraps around the $z$-axis completely.
Therefore, the correct option is (E) Cylinder.