## Calculus (3rd Edition)

Since $$x=r\cos \theta,\quad y=r\cos \theta, \quad z=z,$$ then $$x^2+y^2+z^2=4$$ takes the form $$r^2\cos^2\theta+r^2\sin^2\theta+z^2=r^2+z^2= 4, \quad 0\leq\theta\leq \pi/2.$$ Which is a hemisphere in the first quadrant.