Questions $12-13$ concern the surface $S$ that is the part of the cylinder $x^2+y^2=1$ that satisfies $-\sqrt[\phantom{2}]{1-x^2}z\sqrt[\phantom{2}]{1-x^2}$ and $y0.$

The surface $S$ may be parametrised by the equation

$r(u,v)=cos(u)i+sin(u)j+vk$

Determine the limits for $u$ and $v.$

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No

Calculate the surface area of $S$:${}_{S}1dS.$