find the area of the portion of the sphere z=(1-x^2-y^2)^(1/2) which lies between z=0 and z=1?

my working:

that would be the double integral dS where dS is the area element of S.

i tried to parametrise it then from

double integral dS to integrate from r=0 to 1 then integrate from phi = 0 to pi drdphi...

may i know what is wrong with my working?

thanks!