[tex]x^2+y^2+z^2=2z\implies x^2+y^2+z^2-2z+1=1\implies x^2+y^2+(z-1)^2=1[/tex]
is a sphere centered at (0, 0, 1) with radius 1. We only need to know the radius; the volume is
[tex]V=\dfrac43\pi r^3[/tex]
where [tex]r=1[/tex], so the volume would be [tex]\dfrac{4\pi}3[/tex].
