Describing Level Surfaces

Describe the level surfaces of the function \(w=f(x,y,z)=x^{2}+y^{2}+z^{2}\).

Solution  Since \(w\geq 0\), the level surfaces are the graphs of \[ \begin{equation*} x^{2}+y^{2}+z^{2}=c\qquad c\geq 0 \end{equation*} \]

These are concentric spheres if \(c>0\) and the origin if \(c=0.\) See Figure 16.