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\noindent {\bf Problem statement} A cylinder is inscribed inside a
sphere of radius $R$ (an inscribed cylinder is shown in the picture to
the right). Suppose the height of the cylinder is $x$. Write a formula
for the volume, $V(x)$, of the cylinder as a function of $x$. (This
formula will also include $R$ in some way.) Information about the domain
of $V(x)$ should be part of the explanation. Graph $V(x)$ when $R=3$.

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\noindent {\bf Comment} Label the picture and analyze it carefully. 
 
}

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