Determine the surface area of a ball, rotating a function about $x$-axis.

A football is designed by revolving the graph of $y=\frac{1}{3}x^{\frac{1}{2}}-x^{\frac{3}{2}}$, $0\leq x\leq \frac{1}{3}$, about the $x-$ axis, where $x$ and $y$ are measured in meters. Calculate the surface area of the football.


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Erdos Erdos
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