Why are the contours of a cone equally spaced?

Question

Having trouble understanding what makes the contours of a cone equally spaced, where f(x,y) = root(x^2+y^2).

It would look something like this: http://tutorial.math.lamar.edu/Classes/CalcIII/MultiVrbleFcns_files/image010.gif

Answer 1

$\sqrt{x^2+y^2}$ is the distance between the point $(x,y)$ and the origin $(0,0)$, so the contours are circles of given radius.