Let $\displaystyle k$ be a real number between 0 and $\displaystyle \pi$. Let $\displaystyle R$ be the region in the first quadrant bounded by the x-axis, the line $\displaystyle x=k$ and the curve $\displaystyle y=sin\:x\0\le$$\displaystyle \:x\:$$\displaystyle \le$ $\displaystyle k$). If the volume of the solid generated by revolving the region $\displaystyle R$ about the x-axis is $\displaystyle \frac{\pi}{24}(5\pi-3)$, find the value of $\displaystyle k$.

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