# Using Tikz and spherical coordinates

I would like to show the graph of $f(x,y)=4-x^{2}-y^{2}$ for $x^{2}+y^{2}\leq1,y\geq0$.

I want to draw it using spherical coordinates in Tikz. However I've not found any simple answer for this. Could someone help me?

Something like that?

\documentclass[tikz,border=3.14mm]{standalone}
\usepackage{pgfplots}
\pgfplotsset{compat=1.16}
\begin{document}
\begin{tikzpicture}[declare function={f(\x,\y)=4-\x^2-\y^2;}]
\begin{axis}[view={45}{-45},xlabel={$x$},ylabel={$y$},zlabel={$f(x,y)$}]