\input epsf
\nopagenumbers
\magnification=\magstep1

\noindent {\bf Problem statement} Suppose $R$ is the region in the
plane bounded below by the curve $y=x^2$ and above by the line $y=1$.

\medskip 

\noindent a) Sketch $R$. Set up and evaluate an integral that gives
the area of $R$.

\medskip 

\noindent b) Suppose a solid has base $R$ and the cross-sections of
the solid perpendicular to the $y$-axis are squares. Sketch the solid
and find its volume.

\medskip 

\noindent c) Suppose a solid has base $R$ and the cross-sections of
the solid perpendicular to the $y$-axis are equilateral
triangles. Sketch the solid and find its volume.

\vfil\eject\end

