Answer
See image.
.
Work Step by Step
$ a.\quad$
To sketch the surface $z=f(x,y)=x^{2}+y^{2}$:
* note that z can not be negative (sum of two squares), so the surface is on or above the xy plane
* in a plane $z=k$, the trace is a circle of radius $\sqrt{k}$
* in a plane parallel to $x=0$, the trace is a parabola $z=y^{2}+k$
* in a plane parallel to $y=0$, the trace is a parabola $z=x^{2}+k$
This is an elliptical (circular) paraboloid.
$ b.\quad$
In the xy plane, we equate $f(x,y)$ with several values of c,
$z=x^{2}+y^{2}=c\qquad $(so only nonnnegative c apply)
These are circles with radii $\sqrt{c}.$
Take $c=0,1,2^{2},3^{2}$....
