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t. Let $S$ be the shaded region in the first quadrant bounded above by the|horizontal line $y=3$, below by the graph of $y=3 \sin x$, and on the left by the vertical line $x-k$, where $0<k<\frac{\pi}{2}$, as shown in the figure above. (a) Find the area of $S$ when $k=\frac{\pi}{3}$. b) Let $\mathrm{k}=\frac{\pi}{3}$ Find the volume when $\mathrm{S}$ is revolved around the $\mathrm{x}$-axis. c) Let $k=\frac{\pi}{3}$. Find the volume when $S$ is revolved around the line $y=4$. d) Find the cross section volume when $\mathrm{S}$ is perpendicular to the $\mathrm{x}$ axis and each cross section perpendicular to the $\mathrm{x}$ axis is a square.

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