A fluid has density 900 kg/m³ and flows with velocity $\displaystyle \vec{{{v}}}={x}\vec{{{i}}}+{y}\vec{{{j}}}+{z}\vec{{{k}}}$, where x, y, and z are measured in meters, and the components of $\displaystyle \vec{{{v}}}$ are measured in meters per second. Find the rate of flow outward through the part of the paraboloid $\displaystyle {z}={64}-{x}^{{2}}-{y}^{{2}}$ that lies above the xy plane.

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