Let $L$ be the length of the curve $y=f(x),\,\,a \le x \le b,$ where $f$ is positive and has a continuous derivative. Let $S$ be the surface area generated by rotating the curve about the $x$-axis. If $c$ is a positive constant, define $g(x)=f(x)+c$ and let $T$ be the corresponding surface area generated by the curve $y=g(x),\,\,a \le x \le b.$ Express $T$ in terms of $S$ and $L$.

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