Find the surface area of the upper half of the sphere $x^2 + y^2 + z^2 = 1$ that is inside the (infinite-height) cylinder $x^2 + y^2 - y = 0.$ If the surface of the sphere has mass per unit area equal to |x|, find the mass of the above surface area.
the first line of the solution has already got me stuck, it says that the cylinder equation can be rewritten as $x^2 + (y - \frac12)^2 = \frac12^2$
can someone please explain this to me? I'm not entirely sure how they reached this! :S