(Solved): The figure shows an open cylindrical can, \( S \), standing on the \( x y \)-plane, where the curv ...

The figure shows an open cylindrical can, \( S \), standing on the \( x y \)-plane, where the curve \( C \) is a circle of radius 7 centered on the \( z \)-axis. ( \( S \) has a bottom and sides, but no top.) (a) The equations of the rim \( C \) are: \( x^{2}+y^{2}=49, z=2 \) (b) If \( S \) is oriented outward and downward, \[ \int_{S} \operatorname{curl}(-y \vec{i}+x \vec{j}+z \vec{k}) \cdot d \vec{A}= \] NOTE: Enter the exact answer, or round to three decimal places.