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Let $S$ be the boundary of the portion of the unit sphere that lies in the first octant. Calculate the flux of $\vec{F} = \left\langle x^3, y^3, z^3 \right\rangle$ outward through $S$.

$\cfrac{3\pi}{10}$

$\cfrac{3\pi}{5}$

$\cfrac{\pi}{10}$

$\cfrac{\pi}{15}$

None of the Above